If A and B are two matrices such that $AB = A$ and $BA = B$, then $B^2$ is equal to

B A 1 0

B

We have, $AB = A$ and $BA = B$ $∴B^2 = BB$ $⇒B^2 = (BA) B$   $[∵ BA = B]$ $⇒B^2 = B (AB)$  $[∵ AB = A]$ $⇒B^2 = B$  $[∵ BA = B]$