Question

If for the matrix A, A³ = I, then A⁻¹ = _____________ .

Options

• A²

• A³

• A

• none of these

Answer 1

A²

\[\text{ Given: }\hspace{0.167em} A^3 = I \]

\[ \Rightarrow A^3 A^{- 1} = I A^{- 1}.......... \left[\text{Multiplying both sides by }A^{- 1} \right]\]

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