If A is a square matrix


If $A$ is a square matrix such that $A^{2}=I$, then $A^{-1}$ is equal to

(a) $A+I$

(b) $A$

(c) 0

(d) $2 \mathrm{~A}$


(b) $A$

Given : $A^{2}=I$

On multiplying both sides by $A^{-1}$, we get

$A^{-1} A^{2}=A^{-1} I$

$\Rightarrow A=A^{-1} I$

$\Rightarrow A=A^{-1}$

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