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

A B = B A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A B = 0, B A = I

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A B = B A = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

A B = B A = I

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $A B = B A = I$
We know that if $A$ is a square of order $m$ , and if there exists another square matrix $B$ of the same order $m$ , such that $A B = I$ , 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 $A B = B A = I .$

Suggest Corrections

Similar questions

Q. 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

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 |

Q. Assertion :Let

A = [\begin{matrix} a & b b & a \end{matrix}]

and

B = [\begin{matrix} p & q r & s \end{matrix}]

b = 0

, then

A B = B A

Reason: If

b \neq 0

, then

A B = B A

\Leftrightarrow

p = s a n d q = r

Join BYJU'S Learning Program