Question

$AB=A$ and $BA=B$, then which of the following is not true?

• A. $A$ is idempotent matrix
• B. $B$ is idempotent matrix
• C. $A^T$ is idempotent matrix
• D. None of these

Answer 1

The correct option is D None of these

$AB=A⟹B=I;BA=B⟹A=I⟹A=B=I;A,B,A^T$ are idempotent.