Answer
$A^{-1}=\begin{bmatrix}
\frac{1}{-6}&\frac{1}{-6}&\frac{1}{6}\\
\frac{1}{6}&\frac{-5}{6}&\frac{-7}{6}\\
\frac{5}{6}&\frac{-1}{6}&\frac{-5}{6}
\end{bmatrix}$
Work Step by Step
$det(A)=6$
$C_{11}=-1$, $C_{12}=-1$, $C_{13}=1$, $C_{21}=1$, $C_{22}=-5$, $C_{23}=-7$, $C_{31}=5$, $C_{32}=-1$, $C_{33}=-5$
$A^{-1}=\frac{1}{det(A)}adjA$
$A^{-1}=\begin{bmatrix}
\frac{1}{-6}&\frac{1}{-6}&\frac{1}{6}\\
\frac{1}{6}&\frac{-5}{6}&\frac{-7}{6}\\
\frac{5}{6}&\frac{-1}{6}&\frac{-5}{6}
\end{bmatrix}$
