If A is invertible matrix of order $3\times 3$,then |A|$\neq 0$
The determinant of a matrix should not be equal to zero,it has an inverse.
$A.A^{-1}=I$
$\Rightarrow A^{-1}=\frac{1}{A}.I$
Take determinant on both sides,
$|A^{-1}|=\frac{1}{|A|}|I|$
But |I|=1.
Therefore $|A^{-1}|=\frac{1}{|A|}$