Question

If $A$ is a matrix of order $3\times 3$, then $(A^2{)}^{-1}=$

Answer 1

To find: $(A^2{)}^{-1}=(A\cdot A{)}^{-1}=A^{-1}\cdot A^{-1}$

$[\because (AB{)}^{-1}=B^{-1}{A}^{-1}]$

$=(A^{-1}{)}^2$

Hence, value of $(A^2{)}^{-1}$ is $(A^{-1}{)}^2$.