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  4. If A is a square matrix such that A2 = I, then A-1 is equal to

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

Matrices

Solution:

$A^{2} =I \Rightarrow AA =I \Rightarrow A^{-1} \left(AA\right)=A^{-1} I$
$ \Rightarrow A = A^{-1} $