If A and B are two matrices such that

(a) $B$

Here,

$A B=A \quad \ldots(1)$

$B A=B \quad \ldots(2)$

$\Rightarrow B A B=B B \quad[$ Multiplying both sides by $B]$

$\Rightarrow B A=B^{2} \quad$ [From eq. (1)]

$\Rightarrow B=B^{2} \quad$ [From eq. (2)]