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

Open in App

Solution

Given data is,

A −1 =B B −1 =A

We know that, AA -1 =I AB=I (1)

Also,

BB -1 =I BA=I (2)

From equations (1) and (2), we get

AB=BA = I

Hence, the correct answer is (D).

Suggest Corrections

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. 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 |

Q. If

A

and

B

are square matrices of same order satisfying

A + B = A B,

then

Q. Let A and B be two symmetric matrices. prove that AB=BA if and only if AB is a symmetric matrix.

Q. If A and B are square matrices of the same order, then (A + B)(A − B) is equal to

(a) A² − B²
(b) A² − BA − AB − B²
(c) A² − B² + BA − AB
(d) A² − BA + B²+ AB

Join BYJU'S Learning Program

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

Given data is, A −1 =B B −1 =A We know that, AA -1 =I AB=I (1) Also, BB -1 =I BA=I (2) From equations (1) and (2), we get AB=BA = I Hence, the correct answer is (D).

Given data is,

A −1 =B B −1 =A

We know that, AA -1 =I AB=I (1)

Also,

BB -1 =I BA=I (2)

From equations (1) and (2), we get

AB=BA = I

Hence, the correct answer is (D).