#### Question

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

A + I

A

0

2A

#### Solution

A

\[\text{ Given: }\hspace{0.167em} A^2 = I\]

On multiplying both sides by

\[A^{- 1}\] , we get

\[A^{- 1} A^2 = A^{- 1} I\]

\[ \Rightarrow A = A^{- 1} I\]

\[ \Rightarrow A = A^{- 1}\]

Is there an error in this question or solution?

Solution If A Is a Square Matrix Such That A2 = I, Then A−1 is Equal to Concept: Determinant of a Square Matrix.