Question

A square matrix $A$ is said to be an idempotent matrix if $A^2=A$. If $A$ is a non-singular idempotent matrix, then

• A. $A=I_n$
• B. $A=0$
• C. $A+A^{\prime }=0$
• D. none of these

Answer 1

Answer: (A)

$A=I_n$

$Aisanon-singularidempotentmatrix.i.e{A}^2=AandAisinvertible{A}^{-1}\left(A^2\right)=A^{-1}A\left(A^{-1}A\right)A=I_n\therefore A=I_n$