Question

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

• A. $AB=BA=I$
• B. $AB=0,BA=I$
• C. $AB=BA=0$
• D. $AB=BA$

Answer 1

The correct option is A $AB=BA=I$

Given: $A$ and $B$ will be inverse of each other i.e.
$A^{-1}=B$ and $B^{-1}=A$
We know that
$A{A}^{-1}=I$
$\Rightarrow AB=I\cdots \left(i\right)$
Also,
$B{B}^{-1}=I$
$\Rightarrow BA=I\cdots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$
$AB=BA=I$
So, the correct answer is $D$