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Inverse of a Matrix

If A is a s...

Question

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

I

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O

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A

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I + A

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Solution

The correct option is C $A$
$A^{2} = I$
$A . A = I$
Post multiplying by $A^{- 1}$ both the sides
$A . (A A^{- 1}) = I . A^{- 1}$
$A I = I A^{- 1}$
Hence, $A^{- 1} = A$

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