If A is square matrix such that A^2=A, then (I+A)^3-7 A is equal … - Vidyadip

Question

If $A$ is square matrix such that $A^2=A$, then $(I+A)^3-7 A$ is equal to

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Answer

We have, $(I+A)^3-7 A$
$=I^3+A^3+3 I^2 A+3 I A^2-7 A$
$=1+A \cdot A+3 A+3 A-7 A$
$=1+A+3 A+3 A-7 A$
$=1$

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