CUET Maths Matrix Questions: Important Questions, Topics & Prep Tips

What are the CUET Maths matrix questions?

Direct Answer

Matrices and determinants are the shortest-syllabus, highest-certainty scoring block in the CUET Maths paper — and the only Algebra topic that appears in every version of the paper, whether you sit Mathematics or Applied Mathematics.

This guide gives you 30 exam-level CUET Maths matrix questions with verified answers, the official section-wise topic split, the marks arithmetic behind negative marking, and a 21-day revision plan.

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Key Highlights Before You Start

Point	What it means for you
Matrices sit in Section A1	Section A1 is compulsory for everyone, so you cannot skip matrices by choosing Applied Maths
Matrices appear again in Section B1 and B2	The topic is double-counted — it is the best return on study hours in the paper
Realistic yield	Roughly 3–5 marks-scoring questions per paper across A1 + B1/B2, i.e. 15–25 marks of 250
Time cost	Most matrix MCQs are solvable in 20–45 seconds with the shortcuts in this guide
Negative marking	+5 correct, −1 wrong, 0 unattempted — so a 50/50 guess is still worth attempting

Use the 30 CUET maths matrix important questions in this guide as your benchmark set for the topic.

Also read: CUET 2027 Exam Dates & Overview | CUET Maths Exam Pattern | CUET Syllabus 2027

Download CUET Maths Matrix Questions with Solution PDF

CUET Maths Matrix Questions With Answers (2027 Practice Set)

Every one of these CUET maths matrix questions has had its answer independently verified by symbolic computation.

Give yourself 20 minutes for all 30 — that is 40 seconds each, roughly the pace the real paper demands. These CUET UG maths matrix questions are ordered easy → hard within each set.

Set 1: Types, Order and Basic Properties

Set 1 mirrors the difficulty band of Section A1, so treat these as your baseline CUET maths matrix sample questions — if any of the eight takes more than 30 seconds, that sub-topic needs another pass.

Q1. If A = [2 3 ; 4 5], then Aᵀ is:

(a) [2 3 ; 4 5]

(b) [2 4 ; 3 5]

 (c) [5 4 ; 3 2]

 (d) [5 3 ; 4 2]

Answer: (b) — Rows become columns.

Q2. How many different orders are possible for a matrix with exactly 24 elements?

(a) 6

(b) 8

(c) 12

1. d) 24

 Answer: (b) 8 — Orders correspond to factor pairs of 24, and 24 has 8 divisors.

Q3. A 3×3 matrix A = [aᵢⱼ] is defined by aᵢⱼ = i − j. Then A is:

(a) symmetric

(b) skew-symmetric

(c) a scalar matrix

(d) an identity matrix

Answer: (b) — aⱼᵢ = j − i = −aᵢⱼ, and all diagonal entries are 0.

Q4. If a square matrix A is both symmetric and skew-symmetric, then A must be:

(a) the identity matrix

(b) a diagonal matrix

(c) the null matrix

(d) a singular non-zero matrix

Answer: (c) — A = Aᵀ and A = −Aᵀ force 2A = O.

Q5. A matrix with 5 rows and 4 columns has how many elements?

(a) 9

(b) 16

(c) 20

 (d) 25

 Answer: (c) 20

Q6. How many 3×3 matrices are possible if every entry is either 0 or 1?

(a) 9

(b) 81

 (c) 512

 (d) 1024

Answer: (c) 512 — 2⁹ = 512.

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Q7. The trace of A = [1 −2 ; 3 4] is:

 (a) 5

(b) 3

(c) 2

(d) −5

Answer: (a) 5 — Sum of diagonal entries, 1 + 4.

Q8. If A is skew-symmetric, then A² is:

 (a) skew-symmetric

(b) symmetric

(c) always the null matrix

(d) always singular of order 2

Answer: (b) — (A²)ᵀ = (Aᵀ)² = (−A)² = A².

Set 2: Algebra of Matrices, Transpose and Products

Set 2 is where CUET maths matrix previous year questions cluster most heavily — property-based MCQs that need recall, not calculation.

Q9. For square matrices A and B of the same order, (AB)ᵀ equals:

 (a) AᵀBᵀ

(b) BᵀAᵀ

(c) AB

(d) BA

Answer: (b) BᵀAᵀ

Q10. If A = [2 0 ; 0 3], then A² is:

(a) [4 0 ; 0 9]

(b) [2 0 ; 0 3]

(c) [4 0 ; 0 6]

(d) [6 0 ; 0 6]

 Answer: (a) — For a diagonal matrix, square each diagonal entry.

Q11. If A = [1 1 ; 0 1] and B = [1 0 ; 1 1], then AB − BA equals:

(a) the null matrix

(b) [1 0 ; 0 −1]

(c) [0 1 ; 1 0]

(d) the identity matrix

Answer: (b) — AB = [2 1 ; 1 1], BA = [1 1 ; 1 2]. A clean demonstration that matrix multiplication is not commutative.

Q12. If A = [cos θ −sin θ ; sin θ cos θ], then A·Aᵀ equals:

(a) A

(b) Aᵀ

(c) the identity matrix I

(d) the null matrix

Answer: (c) I — A is orthogonal.

Q13. If [x+y 2 ; 5 xy] = [6 2 ; 5 8], then x² + y² equals:

a) 16

(b) 20

(c) 36

(d) 52

Answer: (b) 20 — x + y = 6, xy = 8, so x² + y² = 36 − 16 = 20.

Download CUET Maths Matrix Revision Notes PDF

Q14. Which of the following is always true for square matrices A and B of the same order?

(a) AB = BA

(b) (A + B)ᵀ = Aᵀ + Bᵀ

(c) (AB)ᵀ = AᵀBᵀ

(d) |A + B| = |A| + |B|

Answer: (b) — Transpose distributes over addition; the other three fail in general.

Set 3: Determinants and Their Properties (Q15–Q22)

Q15. If A is a square matrix of order 3 and |A| = 5, then |2A| equals:

(a) 10

(b) 20

(c) 40

(d) 80

Answer: (c) 40 — |kA| = kⁿ|A| = 2³ × 5.

Q16. The value of |1 2 3 ; 4 5 6 ; 7 8 9| is:

(a) 0

(b) 1

(c) −6

(d) 27

Answer: (a) 0 — R₁ + R₃ = 2R₂, so the rows are linearly dependent.

Q17. If [2 4 ; 1 k] is singular, then k equals:

(a) 1

(b) 2

(c) 4

(d) 8

Answer: (b) 2 — Singular means 2k − 4 = 0.

Q18. The determinant of any skew-symmetric matrix of order 3 is:

(a) 1

(b) −1

(c) 0

d) equal to its trace

Answer: (c) 0 — Every skew-symmetric matrix of odd order is singular.

Q19. If A is of order 3 with |A| = −2, then |A²| equals:

(a) −4

(b) 4

(c) −8

(d) 8

Answer: (b) 4 — |A²| = |A|² = (−2)².

Q20. The cofactor of the element a₁₂ in A = [1 2 ; 3 4] is: (a) 3 (b) −3 (c) 2 (d) −2 Answer: (b) −3 — C₁₂ = (−1)¹⁺² × 3.

Q21. The minor of the element a₂₂ in [1 2 3 ; 4 5 6 ; 7 8 10] is:

(a) 11

(b) −11

(c) −3

(d) 3

Answer: (b) −11 — Delete row 2 and column 2: |1 3 ; 7 10| = 10 − 21.

Q22. The area of the triangle with vertices (1, 0), (6, 0) and (4, 3) is:

(a) 6 sq units

(b) 7.5 sq units

(c) 9 sq units

(d) 15 sq units

Answer: (b) 7.5 sq units — ½|1(0−3) + 6(3−0) + 4(0−0)| = 15/2. (Section B1 candidates only.)

Set 4: Adjoint, Inverse and Systems of Equations (Q23–Q30)

This final set of CUET mathematics matrix questions with solutions covers the sub-topics that carry the most marks per question because they combine two or three properties at once.

Q23. For a square matrix A, A·(adj A) equals:

(a) A

(b) adj A

(c) |A|·I

(d) I

Answer: (c) |A|·I

Q24. If A is of order 3 and |A| = 4, then |adj A| equals

(a) 4

(b) 8

(c) 16

(d) 64

Answer: (c) 16 — |adj A| = |A|ⁿ⁻¹ = 4².

Q25. If A is of order 2 and |A| = 5, then |A·(adj A)| equals:

(a) 5

(b) 10

(c) 25

 (d) 125

Answer: (c) 25 — A·adj A = |A|I, so the determinant is |A|ⁿ = 5².

Q26. If A = [1 2 ; 3 4], then A⁻¹ is:

(a) [−2 1 ; 1.5 −0.5]

(b) [2 −1 ; −1.5 0.5]

(c) [4 −2 ; −3 1]

(d) A⁻¹ does not exist

Answer: (a) — |A| = −2, and A⁻¹ = (1/−2)[4 −2 ; −3 1].

Q27. If A is an invertible matrix of order 3 with |A| = 3, then |A⁻¹| equals:

(a) 3

(b) 1/3

(c) 9

(d) 1/9

 Answer: (b) 1/3 — |A⁻¹| = 1/|A|.

Q28. The solution of x + 2y = 4 and 3x − y = 5 by the matrix method is:

(a) (1, 2)

(b) (2, 1)

(c) (3, 4)

(d) (4, 0)

Answer: (b) (2, 1) — Check: 2 + 2 = 4 ✓ and 6 − 1 = 5 ✓.

Q29. For the system AX = B with |A| = 0 and (adj A)·B ≠ O, the system:

(a) has a unique solution

(b) has infinitely many solutions

(c) has no solution

 (d) cannot be determined

Answer: (c) has no solution — The system is inconsistent.

Q30. If A = [2 −2 −4 ; −1 3 4 ; 1 −2 −3], then A² equals:

 (a) I

b) A

(c) the null matrix

(d) 2A

Answer: (b) A — A is idempotent. Expect this exact matrix (or its close cousins) in property-based CUET UG maths matrix questions.

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How to Read the Matrices in This Guide?

To keep everything copy-paste and mobile-friendly, matrices are written row by row with a semicolon separating rows:

A = [1 2 ; 3 4] means row 1 is 1 2 and row 2 is 3 4.

Where Matrices Actually Sit in the CUET 2027 Maths Paper?

This is the single most misunderstood thing about the Maths paper, and getting it wrong wastes weeks of preparation.

The paper (Subject Code 319) has three labelled sections, not two:

Section	Questions	Marks	Who attempts it
Section A1	15	75	Every candidate, compulsory
Section B1 — Mathematics	35	175	Only core-Mathematics candidates
Section B2 — Applied Mathematics	35	175	Only Applied-Mathematics candidates
You attempt	50	250	Section A1 + either B1 or B2

Two consequences almost nobody plans for:

You do not choose B1 or B2 in the exam hall

The choice is locked by the domain subject you select in the CUET application form. Turning up expecting to pick the easier section is not an option.

Matrices appear in Section A1 and in the Algebra unit of both B1 and B2

No other Algebra topic gets that treatment. If you are hunting for the highest marks-per-hour topic in the paper, this is it — which is why CUET maths matrix questions deserve dedicated practice rather than a single revision pass.

Still deciding between the two streams? See Is Maths and Applied Maths the Same in CUET?

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CUET Maths Exam Pattern 2027

Particular	Detail
Subject name & code	Mathematics / Applied Mathematics — 319
Mode	Computer Based Test (CBT) only
Total questions	50 — all compulsory
Sections attempted	Section A1 (15) + Section B1 or B2 (35)
Duration	60 minutes (+20 min per hour compensatory time for PwBD candidates)
Question type	Objective Multiple Choice Questions (MCQs)
Correct answer	+5
Incorrect answer	−1
Unattempted / marked for review	0
Total marks	250
Max subjects per candidate	5

Important correction to older guides

The "attempt any 40 of 50" format is gone. NTA removed optional questions in the 2026 cycle — all 50 questions are compulsory, and 50 × 5 = 250 marks.

Any article still telling you to attempt 25 of 35 in Section B is describing a pattern that no longer exists.

The negative-marking arithmetic worth memorising

Because marking is asymmetric (+5 / −1), a pure blind guess between four options has an expected value of (0.25 × 5) + (0.75 × −1) = +0.5 marks.

Eliminate even one option and it rises to (1/3 × 5) + (2/3 × −1) = +1.0. Eliminate two and it jumps to +2.0.

For matrices specifically, this matters more than for any other topic: option elimination on matrix MCQs is unusually cheap.

Checking whether a determinant is even or odd, or whether an inverse's entries carry a 1/|A| fraction, often kills two options in five seconds.

That is why practising CUET maths matrix-based MCQs with a timer beats re-reading theory.

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Official Syllabus Checklist: Matrices & Determinants, Section by Section

Tick these off literally. This table is built from the NTA Mathematics/Applied Mathematics syllabus (Code 319), and it is the part most CUET maths matrix important questions lists get wrong. Map every set of CUET maths matrix questions you practise back to this table before you spend time on it.

Sub-topic	Section A1 (all)	Section B1 (Maths)	Section B2 (Applied)
Matrix, order, notation, types of matrices	✅	✅	✅
Equality of matrices	✅	✅	✅
Transpose of a matrix	✅	✅	✅
Symmetric & skew-symmetric matrices	✅	✅	✅
Algebra of matrices (add, subtract, scalar, product)	✅	✅	✅
Non-commutativity; non-zero matrices with zero product	—	✅ (order 2)	—
Invertible matrices; uniqueness of inverse	—	✅	—
Determinant of a square matrix	✅	✅ (up to 3×3)	✅
Minors and cofactors	—	✅	—
Elementary properties of determinants	—	✅	✅
Singular vs non-singular matrix	—	✅	✅
|AB| = |A|·|B|	—	—	✅
Adjoint and inverse of a square matrix	✅ (inverse)	✅	✅ (via cofactors)
(AB)⁻¹ = B⁻¹A⁻¹, (A⁻¹)⁻¹ = A, (Aᵀ)⁻¹ = (A⁻¹)ᵀ	—	—	✅
Area of a triangle using determinants	—	✅	—
Consistency/inconsistency / number of solutions	—	✅	—
Solving simultaneous equations by matrix method	✅	✅ (2–3 variables)	✅ (up to 3 variables)

Two high-value takeaways from this table:

Area of a triangle by determinants is a Section B1 topic only

If you are an Applied Maths (B2) candidate, it is not in your syllabus — several popular CUET maths matrix sample question sets include it for everyone and cost B2 students revision time they do not have.

The three inverse identities (AB)⁻¹ = B⁻¹A⁻¹, (A⁻¹)⁻¹ = A, (Aᵀ)⁻¹ = (A⁻¹)ᵀ are named explicitly in the B2 syllabus

Applied Maths candidates should expect direct property-recall MCQs on them.

Download the official syllabus PDF from cuet.nta.nic.in, and cross-check with our CUET Syllabus 2027 breakdown.

Quick Answer Key

Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	b	6	c	11	b	16	a	21	b	26	a
2	b	7	a	12	c	17	b	22	b	27	b
3	b	8	b	13	b	18	c	23	c	28	b
4	c	9	b	14	b	19	b	24	c	29	c
5	c	10	a	15	c	20	b	25	c	30	b

Each item above is a set of CUET mathematics matrix questions with solutions rather than a bare answer key, so read the one-line reasoning even on the questions you got right.

Score yourself: 26–30 correct → matrices are exam-ready, move on. 18–25 → revise determinant properties, then re-attempt. Below 18 → go back to NCERT Class 12 Chapters 3 and 4 before attempting more CUET maths matrix-based MCQs.

Want the full paper context? Practise with CUET Maths Question Papers and the wider CUET Previous Year Question Papers.

The 8 Formulas That Answer Most Matrix MCQs in Under 30 Seconds

#	Result	Use it when
1	|kA| = kⁿ|A| (n = order)	A scalar multiplies the whole matrix
2	|adj A| = |A|ⁿ⁻¹	Adjoint determinant asked directly
3	A·adj A = adj A·A = |A|·I	Any adjoint-product question
4	|A⁻¹| = 1/|A|	Inverse determinant asked
5	|Aᵀ| = |A| and |AB| = |A||B|	Transpose or product determinants
6	(AB)ᵀ = BᵀAᵀ; (AB)⁻¹ = B⁻¹A⁻¹	Order reverses — the most-tested trap
7	Skew-symmetric of odd order ⇒ |A| = 0	Any odd-order skew-symmetric matrix
8	|A| = 0 and (adj A)B ≠ O ⇒ no solution	Consistency of AX = B

Write these on one index card. In a 60-minute paper, recall beats derivation every single time — most CUET maths matrix questions are decided by which of these eight results you recognise first, not by how fast you can compute.

5 Traps That Quietly Cost Students Marks

1. Reversing the order. (AB)ᵀ = BᵀAᵀ, not AᵀBᵀ. The same reversal applies to inverses. Option (c) in Q9 and Q14 exists purely to catch this.

2. Forgetting the exponent in |kA|. Students multiply the determinant by k instead of kⁿ. In Q15, that turns 40 into 10 — and option (a) is waiting.

3. Assuming AB = O implies A = O or B = O. The NTA syllabus names this explicitly for order 2. It is false, and it is examined.

4. Treating "singular" as "no determinant". Singular means the determinant equals zero, which is exactly what makes Q17 solvable in five seconds.

5. Studying the wrong section. B2 candidates grinding through area-of-triangle problems, or B1 candidates memorising |AB| = |A||B| as an Applied-Maths-only identity. Use the syllabus checklist above.

None of these appears in generic CUET maths matrix sample question collections, which is precisely why they keep working as distractors. They do, however, show up repeatedly in CUET maths matrix previous year questions.

21-Day Matrices & Determinants Revision Plan

Days	Focus	Daily output
1–3	NCERT Ch. 3: types, equality, transpose, symmetric/skew-symmetric	15 MCQs
4–6	Algebra of matrices, non-commutativity, AB = O cases	15 MCQs
7–9	NCERT Ch. 4: determinants, elementary properties, singular matrices	20 MCQs
10–12	Minors, cofactors, adjoint	20 MCQs
13–15	Inverse; the three inverse identities; |adj A| and |kA|	20 MCQs
16–18	Systems of equations; consistency; (B1 only) area of a triangle	20 MCQs + 1 sectional test
19–21	Timed revision: the 8-formula card + this 30-question set, twice	2 full attempts under 20 min

Three weeks, roughly 30 minutes a day, and by day 21 you should be clearing 30 CUET UG maths matrix questions inside 20 minutes.

If you are building a full subject plan around this, pair it with How to Score 700+ in CUET and CUET Preparation for Average Students.

Download CUET 2027 Subject Wise Syllabus PDFs

Books and Official Resources We Actually Recommend

Resource	Use it for
NCERT Class 12 Maths, Chapters 3 & 4	Non-negotiable base — the syllabus is written from it
NCERT Exemplar, Chapters 3 & 4	MCQ-style and assertion-reason practice
NCERT Class 12 Applied Maths, Unit II	B2 candidates: the three inverse identities and |AB|
Official syllabus PDF, Code 319 (cuet.nta.nic.in)	Confirming what is and is not in your section
Past CUET Maths papers	Calibrating difficulty and question phrasing
This page's 30-question set	Ready CUET mathematics matrix questions with solutions for timed revision

Compare editions and levels on our Best Books for CUET Maths and CUET Preparation Books pages.

Next Steps

CUET maths matrix questions are the rare CUET topic where three weeks of focused work produces a near-certain return, because the chapter is short, the syllabus is explicit, and the question styles repeat.

Work through the 30 CUET maths matrix important questions above under a timer, memorise the eight-formula card, and re-attempt the set in week three.

Then move on to mixed CUET maths matrix based MCQs from full-length papers.

If you want the same treatment applied to every unit in the paper, our faculty build subject-wise plans inside SuperGrads CUET Online Coaching.

You can also compare options first on Best Coaching for CUET 2027, or read Can I Crack CUET Without Coaching? if you would rather self-study.

• NCERT Class 12 Mathematics (Ch. 3–4) and Applied Mathematics (Unit II) — topic scope
• All 30 answers independently verified by symbolic computation, 27 July 2026

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