Answer
$\frac{1}{3}$.
Work Step by Step
If $A$ and $B$ are $n\times n$ matrices, then $det(A^{-1})=\frac{1}{det(A)}$ if $det(A)\ne0$.
Hence here $det(A^{-1})=\frac{1}{det(A)}=\frac{1}{3}$.
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