If $AB=A$ and $BA=B$, then $B^2$ is equal to

The correct option is A

$B$

Explanation for the correct option:

Find the value of $B^2$:

Given, $AB=A$ and $BA=B$

multiply both sides by $B$

$BA\times B=B\times B$

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

$\Rightarrow$ $B\left(A\right)=B^2$ $\left[\because BA=B\right]$

$\Rightarrow$ $B=B^2$

$\mathbf{\therefore }{\mathit{B}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathit{B}$

Hence, option ‘A’ is Correct.