Answer
$A^{-1}=\begin{bmatrix}
\frac{-1}{6}&\frac{-1}{6}&\frac{5}{6}\\
\frac{1}{6}&\frac{-5}{6}&\frac{1}{6}\\
\frac{1}{6}&\frac{7}{6}&\frac{-5}{6}
\end{bmatrix}$
Work Step by Step
$det(A)=6$
Matrix of Cofactors:
$C=\begin{bmatrix}
{-1}&{1}&{1}\\{-1}&{-5}&{7}\\{5}&{1}&{-5}
\end{bmatrix}$
After transposing, Adjugate matrix:
$adj(A)=\begin{bmatrix}
{-1}&{-1}&{5}\\{1}&{-5}&{1}\\{1}&{7}&{-5}
\end{bmatrix}$
$A^{-1}=\frac{1}{det(A)}adjA$
$A^{-1}=\begin{bmatrix}
\frac{-1}{6}&\frac{-1}{6}&\frac{5}{6}\\
\frac{1}{6}&\frac{-5}{6}&\frac{1}{6}\\
\frac{1}{6}&\frac{7}{6}&\frac{-5}{6}
\end{bmatrix}$
