Question

If $A$ is square matrix such that $A^2=1$ then $A^{-1}=?$

• A. $2$A
• B. A
• C. $0$
• D. A+$1$

Answer 1

Answer: (B)

A

$A^2=1$ can be witten as

$A^2=I$

multiply $A^{-1}$ on both side

$A^{-1}\times (A\times A)=A^{-1}\times I(A^{-1}\times A)\times A=A^{-1}I\times A=A^{-1}{A}^{-1}=A$

Corrrect option is B