If A and B are two matrices such that $AB = A$ and $BA = B$, then $B^2$ is equal to
Answer & explanation
Correct answer: option 1
We have, $AB = A$ and $BA = B$
$∴B^2 = BB$
$⇒B^2 = (BA) B$ $[∵ BA = B]$
$⇒B^2 = B (AB)$ $[∵ AB = A]$
$⇒B^2 = B$ $[∵ BA = B]$