Question

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

Options

• A + I

• A

• 0

• 2A

Answer 1

A

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

On multiplying both sides by

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

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

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

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