Question

If $AB=A,BA=B$ for any two square matrices $A$ and $B$, then $A^2$ is equal to

• A. A
• B. B
• C. AB
• D. $B^2$

Answer 1

Answer: (D)

Given, $AB=A\Rightarrow B=I$
and $BA=B\Rightarrow A=I$
Now, $A^2=A.A$ $=AB.A$
$=A.BA$ $=I.B$
$=B.B=B^2$