If A is a square matrix and A^2=A, then (I+A)^2-3 A is equal to - Vidyadip

Question

If $A$ is a square matrix and $A^2=A$, then $(I+A)^2-3 A$ is equal to

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Answer

Given that $A^2=A$
$\text { Consider }(I+A)^2-3 A$
$=I^2+A^2+2 A I-3 A$
$=I+A+2 A-3 A \quad\left[\because I^2=I, A^2=A \text { (given) }\right]$
$=1$

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