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)

B

Answer 2

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