Question

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

• A. A
• B. B
• C. I
• D. 0

Answer 1

Answer: (B)

Since $BA=B\therefore (BA)B=(B)(B)=B^2$
$\Rightarrow B(AB)=B^2\Rightarrow BA=B^2$ $[\because AB=A]$
$\Rightarrow B=B^2[\because BA=B]$