Question: If for the matrix $A, A^{3}=1$, then $A^{-1}=$
(a) $A^{2}$
(b) $A^{3}$
(c) $A$
(d) none of these
Solution:
(a) $A^{2}$
Given : $A^{3}=I$
$\Rightarrow A^{3} A^{-1}=I A^{-1} \quad$ [Multiplying both sides by $\left.A^{-1}\right]$
$\Rightarrow A^{2}=A^{-1}$
