Question

Let $A$ be a square matrix such that $A^2=A$ and $|A|\ne 0$, then choose the correct option.

(A' represents transpose of matrix A)

• A. $A=A^{\prime }$
• B. $A=-A^{\prime }$
• C. $A^{\prime }=-I$
• D. $A=-I$

Answer 1

Answer: (A)

$A=A^{\prime }$

$A$ is a square matrix such that $A^2=A$ and $|A|\ne 0$
$\Rightarrow A^{-1}{A}^2=A^{-1}A=I$
$\Rightarrow A=I$
$\therefore A=A^{\prime }=I$
Hence, option A.