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Practice 68 Matrices questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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About Matrices — practice questions, PYQs & concepts

Matrices is a frequently-tested topic on Mathematics. ExamTest.live currently lists 68 Matrices questions spanning previous-year papers from 2004 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Matrices weight in competitive exams

Across our Matrices question bank, the largest sources are Mathematics (68). Click any exam chip above to drill down to that exam-specific question set.

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All Matrices Questions(1–68 of 68)

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Q1mediummcqMathematicsMathematics Mock Test - 62026

4% accuracy

If A = [0110] and B = [0 i - i 0], then (A + B) (A + B) is equal to:

Q2mediummcqMathematicsMathematics Mock Test - 62026

4% accuracy

The system of equations: αx + y + z = α - 1 x + α y + z = α - 1 x + y + α z = α - 1 has no solution, if α is:

Q3mediummcqMathematicsMathematics Mock Test - 62026

4% accuracy

If a + b b + c c + a b + c c + a a + b c + a a + b b + c = K a b c b c a c a b, then K =

Q4mediummcqMathematicsMathematics Mock Test - 62026

17% accuracy

If A = [03 2 - 4] and k A = [0 2 b 3 a 24], then the values of k, a, b are respectively:

Q5mediummcqMathematicsMathematics Mock Test - 62026

13% accuracy

If A = [14 - 2 5] and f (t) = t^{2} - 3 t + 7, then f (A) + [3 - 12 6 - 9] is equal to:

Q6mediummcqMathematicsMathematics Mock Test - 62026

9% accuracy

The order of [x y z] a h g h b f g f c x y z is:

Q7mediummcqMathematicsMathematics Mock Test - 12026

9% accuracy

If A = (2924) and I = (1001), then 10 A^{- 1} is equal to:

Q8mediummcqMathematicsMathematics Mock Test - 12026

0% accuracy

If A and B are two matrices such that A B = B and B A = A, then A^{2} + B^{2} is equal to:

Q9mediummcqMathematicsMathematics Mock Test - 102026

18% accuracy

The number of 2 \times 2 matrices A, with each element as a real number and satisfying A + A^{T} = I and A^{T} A = I, is:

Q10mediummcqMathematicsMathematics Mock Test - 102026

36% accuracy

If f (α) = [cos α - sin α sin α cos α] and if α, β and γ are angles of a triangle, then x is a solution to x^{n} = ∣ f (α) \cdot f (β) \cdot f (γ) ∣ where n = 3 . What are the values of x ?

Q11hardmcqMathematicsMathematics Mock Test - 102026

18% accuracy

Given matrix A = 113 - 2 16 1 - 1 - 5 and adj A = 123 - 4 8 - 12 123, the system of equations: x - 2 y + z = 5 x + y - z = 6 3 x + 6 y - 5 z = 7 has:

Q12mediummcqMathematicsMathematics Mock Test - 52026

50% accuracy

If 2 A + 3 B = [23 - 1 2 45] and A + 2 B = [510632], then matrix B is:

Q13mediummcqMathematicsMathematics Mock Test - 52026

100% accuracy

The set of equations a + b - 2 c = 0, 2 a - 3 b + c = 0, and a - 5 b + 4 c = α is consistent. If the cofactors of the coefficient matrix A are C_{11} = 7, C_{12} = - 7, C_{13} = 7, C_{21} = 6, C_{22} = - 6, C_{23} = 6, C_{31} = 5, C_{32} = - 5, C_{33} = 5, find the value of α .

Q14mediummcqMathematicsMathematics Mock Test - 52026

50% accuracy

Let A = [1 - 5 21] and A^{- 1} = x A + y I, then the values of x and y are:

Q15mediummcqMathematicsMathematics Mock Test - 52026

50% accuracy

The co-factor of the element '4' in the determinant 1280330254111211

Q16mediummcqMathematicsMathematics Mock Test - 52026

0% accuracy

If a \neq = 6, b, c satisfy a 34 2 b b a 2 c c b = 0 then ab c =

Q17mediummcqMathematicsMathematics Mock Test - 52026

0% accuracy

If O (A) = 2 \times 3, O (B) = 3 \times 2 and O (C) = 3 \times 3, which one of the following is not defined?

Q18mediummcqMathematicsMathematics Mock Test - 52026

0% accuracy

If for a matrix A, A^{2} + I = 0, where I is the identity matrix of order 2, then A can be:

Q19mediummcqMathematicsMathematics Mock Test - 42026

0% accuracy

If A = 200020002, then A^{5} is equal to:

Q20mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

If A is a singular matrix, then adj A is:

Q21mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

If I_{3} is the identity matrix of order 3, then I_{3}^{- 1} is:

Q22mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

Find the condition on k, so that the system of equations: x + 3 y = 5 and 2 x + k y = 8 has a unique solution.

Q23mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

The value of k for which the system of equations x + k y + 3 z = 0, 4 x + 3 y + k z = 0, 2 x + y + 2 z = 0 has a non-trivial solution is:

Q24mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

If a_{ij} = \frac{1}{2} (3 i - 2 j) and A = [a_{ij}]_{2 \times 2}, then A is equal to:

Q25mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

Let A = 431 60 - 2 - 1 25, B = 2 - 1 1 042, and C = [312] . The expression which is not defined is:

Q26mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

If the area of a triangle with vertices (- 3, 0), (3, 0) and (0, k) is 9 square units, then what is the value of k ?

Q27mediummcqMathematicsMathematics Mock Test - 42026

0% accuracy

If A is a skew-symmetric matrix, then its transpose A^{T} is equal to:

Q28mediummcqMathematicsMathematics Mock Test - 42026

0% accuracy

Find the value of det (2^{2} A) for the following matrix: A = 2 - 1 - 3 301122

Q29mediummcqMathematicsAIEEE 20072026

100% accuracy

Let A = [5 α 0 α α] . If ∣ A^{2} ∣ = 25, then ∣ α ∣ equals:

Q30mediummcqMathematicsAIEEE 20072026

0% accuracy

If D = 111 1 1 + x 1 11 1 + y for x \neq = 0, y \neq = 0, then D is:

Q31mediummcqMathematicsAIEEE 20062026

0% accuracy

Let A = (1324) and B = (a 0 0 b), a, b \in N . Then:

Q32mediummcqMathematicsAIEEE 20062026

0% accuracy

If A and B are square matrices of size n \times n such that A^{2} - B^{2} = (A - B) (A + B), then which of the following will be always true?

Q33mediummcqMathematicsMathematics Mock Test - 92026

0% accuracy

If U = [2, - 3, 4], X = [0, 2, 3], V = 321 and Y = 224, then U V + X Y =

Q34mediummcqMathematicsMathematics Mock Test - 92026

0% accuracy

If A = 200020002 and B = 100210332, then ∣ A B ∣ is equal to:

Q35mediummcqMathematicsMathematics Mock Test - 42026

100% accuracy

The order of a matrix is defined as:

Q36mediummcqMathematicsMathematics Mock Test - 82026

The minors of - 4 and 9 and the co-factors of - 4 and 9 in the determinant - 1 - 4 - 7 - 2 - 5 - 8 3 - 6 9 are respectively:

Q37mediummcqMathematicsMathematics Mock Test - 82026

If X = [31 - 4 - 1], then the value of X^{n} is:

Q38mediummcqMathematicsMathematics Mock Test - 82026

If f (x) = [x 2 λ λ x], then ∣ f (λ x) - f (x) ∣ is equal to:

Q39mediummcqMathematicsMathematics Mock Test - 32026

M is a square matrix of order n and ∣ M ∣ = 5 . If all elements of M are multiplied by 2, the determinant becomes 40 . The value of n is:

Q40mediummcqMathematicsMathematics Mock Test - 82026

The real value of k for which the system of equations 2 k x - 2 y + 3 z = 0, x + k y + 2 z = 0, 2 x + k z = 0, has a non-trivial solution is:

Q41mediummcqMathematicsMathematics Mock Test - 82026

The values of x for which the given matrix - x 2 x x x - 2 2 - x - x will be non-singular are:

Q42mediummcqMathematicsMathematics Mock Test - 82026

If A = 103 - 2 2 - 2 2 - 3 4, then A \cdot adj (A) is equal to:

Q43mediummcqMathematicsMathematics Mock Test - 112026

If A = [64 - 3 - 2] and B = [2 x y 7], such that A B = O (Zero matrix), find the values of x and y .

Q44mediummcqMathematicsAIEEE2026

Let A be a 2 \times 2 matrix with non-zero entries and let A^{2} = I .Statement-1: Tr (A) = 0 Statement-2: ∣ A ∣ = 1

Q45mediummcqMathematicsAIEEE2026

The system of equations: αx + y + z = α - 1, x + α y + z = α - 1, x + y + α z = α - 1 has no solution, if α is:

Q46mediummcqMathematicsAIEEE2026

If A = [1101] and I = [1001], then which one of the following holds for all n \geq 1 ?

Q47mediummcqMathematicsAIEEE2026

If a^{2} + b^{2} + c^{2} = - 2 and f (x) = 1 + a^{2} x (1 + a^{2}) x (1 + a^{2}) x (1 + b^{2}) x 1 + b^{2} x (1 + b^{2}) x (1 + c^{2}) x (1 + c^{2}) x 1 + c^{2} x, then f (x) is a polynomial of degree:

Q48mediummcqMathematicsAIEEE2026

If a_{1}, a_{2}, a_{3}, \dots, a_{n}, \dots are in G.P., then the determinant Δ = lo g a_{n} lo g a_{n + 3} lo g a_{n + 6} lo g a_{n + 1} lo g a_{n + 4} lo g a_{n + 7} lo g a_{n + 2} lo g a_{n + 5} lo g a_{n + 8} is equal to:

Q49mediummcqMathematicsAIEEE-CBSE-ENG-032026

If A = [a b b a] and A^{2} = [α β β α], then:

Q50mediummcqMathematicsAIEEE-CBSE-ENG-032026

If 1, ω, ω^{2} are the cube roots of unity, then Δ = 1 ω^{n} ω^{2 n} ω^{n} ω^{2 n} 1 ω^{2 n} 1 ω^{n} is equal to:

Q51mediummcqMathematicsAIEEE2026

Let A be a 2 \times 2 matrix with real entries. Let I be the 2 \times 2 identity matrix. Denote by tr (A) the sum of diagonal entries of A . Assume A^{2} = I .Statement - 1: If A \neq = I and A \neq = - I, then det A = - 1 .Statement - 2: If A \neq = I and A \neq = - I, then tr (A) \neq = 0 .

Q52mediummcqMathematicsAIEEE2026

Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

Q53mediummcqMathematicsAIEEE 20092026

1: adj (adj A) = A where A is a 2 \times 2 matrix. 2: ∣ adj A ∣ = ∣ A ∣ .

Q54hardmcqMathematicsAIEEE2026

The number of 3 \times 3 non-singular matrices, with four entries as 1 and all other entries as 0, is:

Q55mediummcqMathematicsMathematics Mock Test - 32026

The system of equations x + 2 y + z = 0, x - z = k, x + y = 0 has infinitely many solutions. If adj (A) = 1 - 1 1 1 - 1 1 - 2 2 - 2, then the possible value of k is:

Q56easymcqMathematicsAIEEE2026

Consider the system of linear equations: x_{1} + 2 x_{2} + x_{3} = 3 2 x_{1} + 3 x_{2} + x_{3} = 3 3 x_{1} + 5 x_{2} + 2 x_{3} = 1 The system has:

Q57mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026

The number of values of k for which the linear equations 4 x + k y + 2 z = 0, k x + 4 y + z = 0, and 2 x + 2 y + z = 0 possess a non-zero solution is:

Q58mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026

Let A and B be two symmetric matrices of order 3 .Statement-1 : A B A and A B^{2} A are symmetric matrices.Statement-2 : A B is a symmetric matrix if matrix multiplication of A and B is commutative.

Q59mediummcqMathematicsAIEEE 20122026

Let A = 123012001 . If u_{1} and u_{2} are column matrices such that A u_{1} = 100 and A u_{2} = 010, then u_{1} + u_{2} is equal to:

Q60mediummcqMathematicsAIEEE 20122026

Let P and Q be 3 \times 3 matrices with P \neq = Q . If P^{3} = Q^{3} and P^{2} Q = Q^{2} P, then determinant of (P^{2} + Q^{2}) is equal to:

Q61mediummcqMathematicsJEE Main2026

If P = 112 α 34 334 is the adjoint of a 3 \times 3 matrix A and ∣ A ∣ = 4, then α is equal to:

Q62mediummcqMathematicsMathematics Mock Test - 32026

If [1 x 1] 143252365 1 - 2 3 = 0, then the value of x is:

Q63mediummcqMathematicsAIEEE2026

If A^{2} - A + I = 0, then the inverse of A is:

Q64mediummcqMathematicsMathematics Mock Test - 32026

Which of the following is NOT true for matrices A, B, C (assuming dimensions allow operations)?

Q65mediummcqMathematicsMathematics Mock Test - 32026

If a matrix A is such that 3 A^{3} + 2 A^{2} + 5 A + I = O, then what is A^{- 1} equal to?

Q66mediummcqMathematicsMathematics Mock Test - 32026

If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B ?

Q67easymcqMathematicsAIEEE 20042004

0% accuracy

Let A = 00 - 1 0 - 1 0 - 1 00 . The only correct statement about the matrix A is

Q68mediummcqMathematicsAIEEE 20042004

0% accuracy

Let A = 121 - 1 11 1 - 3 1 and 10 B = 4 - 5 1 20 - 2 2 a 3 . If B is the inverse of matrix A, then a is

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