Matrices A and B will be inverse of each other only if

A. AB = BA

C. AB = 0, BA = I

B. AB = BA = 0

D. AB = BA = I

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Solution

Answer: D

We know that if A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is said to be the inverse of A. In this case, it is clear that A is the inverse of B.

Thus, matrices A and B will be inverses of each other only if AB = BA = I.

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Similar questions

Choose the correct answer in the following question.
Matrices A and B will be inverse of each other only if
(a)AB=BA
(b)AB =BA =O
(c)AB=O, BA=I
(d)AB=BA =I

Q. If

A

and

B

are square matrices of same order satisfying

A + B = A B,

then

Q. Assertion : If

A

is a non-singular matrix, then

| A^{-} 1 | = \frac{1}{| A |}

Reason : If

A

and

B

are inverse matrices of each other , then

A B = B A = I

and

| A B | = | A | | B |

I f A, B

are symmetric matrices of the same order then

A B - B A

A

and

B

are symmetric matrices of the same order.

X = A B + B A

and

Y = A B - B A

(X Y)^{T} =

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Matrices A and B will be inverse of each other only if A. AB = BA C. AB = 0, BA = I B. AB = BA = 0 D. AB = BA = I

Matrices A and B will be inverse of each other only if

A. AB = BA

C. AB = 0, BA = I

B. AB = BA = 0

D. AB = BA = I