Question

If $A$ is a square matrix such that $A^2=A$, then $det\left(A\right)$ equals

• A. $-1$ or $1$
• B. $-2$ or $2$
• C. $-3$ or $3$
• D. None of these

Answer 1

The correct option is D None of these

Given, $A^2=A$

$A^2-A=0$

$\Rightarrow |A^2-A|=0$

$\Rightarrow |A(A-I)|=0$

$\Rightarrow |A||A-I|=0$

$\Rightarrow |A|=0or|A-I|=0$

$\Rightarrow |A|=0,or|A|=1$