Question

A and B are two matrices such that AB = A and BA = B then what is $B^2$ equal to ?
Where I is the identity matrix.

• A. B
• B. A
• C. I
• D. -I

Answer 1

The correct option is A B

Now here $AB=A$ and $BA=B$

$BA=B$, Multiplying by matrix $B$, we get

$BAB=B^2$

$\Rightarrow B\left(AB\right)=B^2$

$\Rightarrow BA=B^2$ ...... $[\because AB=A]$

$\Rightarrow B=B^2$ ...... $[\because BA=B]$

Hence, option A is correct.