250+ TOP MCQs on Inverse of Matrices and Answers

Discrete Mathematics Multiple Choice Questions on “Inverse of Matrices”.

1. For a matrix A, B and identity matrix I, if a matrix AB=I=BA then?
a) B is inverse of A
b) A is inverse of B
c) A^-1 = B, B^-1 = A
d) All of the mentioned

Answer: d
Clarification: Since AB = I, A = B^-1 Similarly A is the inverse of B.

2. For matrix A,(A³) = I, A^-1 is equals to _________
a) A²
b) A^-2
c) Can’t say
d) None of the mentioned

Answer: a
Clarification: A(A²) = I this implies A^-1 = A².

3. Let A = [0 1 0 0 ], A^-1 is equal to _________
a) Null matrix
b) Identity matrix
c) Does not exist
d) None of the mentioned

Answer: c
Clarification: Since A is singular matrix, inverse does not exists.

4. If A is an invertible square matrix then _________
a) (A^T)^-1 = (A^-1)^T
b) (A^T)^T = (A^-1)^T
c) (A^T)^-1 = (A^-1)^-1
d) None of the mentioned

Answer: a
Clarification: For invertible matrix A, A^T is also inveritble.

5. If matrix A, B and C are invertible matrix of same order then (ABC)^-1 = _________
a) CBA
b) C^-1 B^-1 A^-1
c) C^T B^-1 A^T
d) None of the mentioned

Answer: b
Clarification: Reversal rule holds for inverse multiplication of the matrices.

6. If A is non singular matrix then AB = AC implies B = C.
a) True
b) False

Answer: a
Clarification: Pre-multipliying by A^-1 we get B = C.

7. For a matrix A of order n, the det(adj(A)) = (det(A))ⁿ, where adj() is adjoint of matrix.
a) True
b) False

Answer: b
Clarification: For a matrix A of order n, the det(adj(A)) = (det(A))^n-1.

8. For a non-singular matrix A, A^-1 is equal to _________
a) (adj(A))/det(A)
b) det(A)*(adj(A))
c) det(A)*A
d) none of the mentioned

Answer: a
Clarification: A(adj(A)) = det(A)I, I = A(adj(A))/det(A) which implies A^-1 = (adj(A))/det(A).

9. Let I₃ be the Identity matrix of order 3 then (I₃)^-1 is equal to _________
a) 0
b) 3I₃
c) I₃
d) None of the mentioned

Answer: c
Clarification: Idenity matrices are self invertible that is I₃ x I₃ = I₃.

10. If for a square matrix A(non-singular) and B, null matrix O, AB = O then?
a) B is a null matrix
b) B is a non singular matrix
c) B is a identity matrix
d) All of the mentioned

Answer: a
Clarification: Given det(A) is not equal to zero. A-1 exists, A^-1(AB) = O, B = O.