Answer
$$\operatorname{adj}(A)=\left[ \begin {array}{cccc} 7&1&9&-13\\ 7&1&0&-4
\\ -4&2&-9&10\\ 2&-1&9&-5
\end {array} \right]
.$$
$$A^{-1}=\frac{1}{9}\left[ \begin {array}{cccc} 7&1&9&-13\\ 7&1&0&-4
\\ -4&2&-9&10\\ 2&-1&9&-5
\end {array} \right].$$
Work Step by Step
The matrix is given by $A=\left[ \begin {array}{cccc} -1&2&0&1\\ 3&-1&4&1
\\ 0 &0&1&2\\ -1&1&1&2\end {array}
\right]
.$
To find $\operatorname{adj}(A)$, we calculate first the cofactor matrix of $A$ as follows
$$\left[ \begin {array}{cccc} 7&7&-4&2\\ 1&1&2&-1
\\ 9&0&-9&9\\ -13&-4&10&-5
\end {array} \right]
.$$
Now, the adjoint of $A$ is
$$\operatorname{adj}(A)=\left[ \begin {array}{cccc} 7&1&9&-13\\ 7&1&0&-4
\\ -4&2&-9&10\\ 2&-1&9&-5
\end {array} \right]
.$$
To find $A^{-1}$, we have to calculate $\det(A)$ which is given by
$$\det(A)=9.$$
Finally, we have
$$A^{-1}=\frac{1}{\det(A)}\operatorname{adj}(A)=\frac{1}{9}\left[ \begin {array}{cccc} 7&1&9&-13\\ 7&1&0&-4
\\ -4&2&-9&10\\ 2&-1&9&-5
\end {array} \right].$$
