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) (AT)-1 = (A-1)T
b) (AT)T = (A-1)T
c) (AT)-1 = (A-1)-1
d) None of the mentioned

Answer: a
Clarification: For invertible matrix A, AT 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) CT B-1 AT
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.

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