Question

If A is a square matrix such that A² = I, then A⁻¹ is equal to
(a) A + I
(b) A
(c) 0
(d) 2A

Answer 1

(b) A

$\mathrm{Given}:\hspace{0.17em}{A}^2=I$
On multiplying both sides by $A^{-1}$ , we get

$$\begin{gathered} A^{-1}{A}^2=A^{-1}I \\ \Rightarrow A=A^{-1}I \\ \Rightarrow A=A^{-1} \end{gathered}$$