This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses 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

View Answer

Explanation: Since AB = I, A = B

^{-1}Similarly A is the inverse of B.

2. For matrix A,(A^{3}) = I, A^{-1} is equals to:

a) A^{2}

b) A^{-2}

c) Can’t say

d) None of the mentioned

View Answer

Explanation: A(A

^{2}) = I this implies A

^{-1}= A

^{2}.

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

View Answer

Explanation: 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

View Answer

Explanation: 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}

4) None of the mentioned

View Answer

Explanation: Reversal rule holds for inverse multiplication of the matrices.

6. State True or False?

If A is non singular matrix then AB = AC implies B = C.

a) True

b) False

View Answer

Explanation: Pre-multipliying by A

^{-1}we get B = C.

7. State True or False:

For a matrix A of order n, the det(adj(A)) = (det(A))^{n}, where adj() is adjoint of matrix.

a) True

b) False

View Answer

Explanation: 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

View Answer

Explanation: A(adj(A)) = det(A)I, I = A(adj(A))/det(A)which implies A

^{-1}= (adj(A))/det(A).

9. Let I_{3} be the Identity matrix of order 3 then (I_{3})^{-1} is equal to:

a) 0

b) 3I_{3}

c) I_{3}

d) None of the mentioned.

View Answer

Explanation: Idenity matrices are self invertible that is I

_{3}x I

_{3}= I

_{3}.

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

View Answer

Explantion: Given det(A) is not equal to zero. A-1 exists, A

^{-1}(AB) = O, B = O.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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