Question

If for the non-singular matrix $A,A^2=I$, then find $A^{-1}$.

• A. $A$
• B. $I$
• C. $O$
• D. None of these

Answer 1

Answer: (A)

Given, $A^2=I$
Since, A is non-singular matrix
$\therefore \left|A\right|\ne 0,so,A^{-1}$ exists.
Multiplying by $A^{-1}$ on both sides, we get
$A^{-1}\left(A^2\right)=A^{-1}\left(I\right)$
$\Rightarrow \left(A^{-1}A\right)A=A^{-1}\Rightarrow IA=A^{-1}\left(\because A^{-1}A=I\right)$
$\therefore A^{-1}=A\left(\because IA=A\right)$