Answer
$$\operatorname{adj}(A)=\left[ \begin {array}{ccc} -7&-12&13\\ 2&3&-5
\\ 2&3&-2\end {array} \right]
.$$
$$A^{-1}= -\frac{1}{3}\left[ \begin {array}{ccc} -7&-12&13\\ 2&3&-5
\\ 2&3&-2\end {array} \right].$$
Work Step by Step
The matrix is given by $A=\left[ \begin {array}{ccc} -3&-5&-7\\ 2&4&3
\\ 0&1&-1\end {array} \right]
.$
To find $\operatorname{adj}(A)$, we calculate first the cofactor matrix of $A$ as follows
$$\left[ \begin {array}{ccc} -7&2&2\\ -12&3&3
\\ 13&-5&-2\end {array} \right]
.$$
Now, the adjoint of $A$ is
$$\operatorname{adj}(A)=\left[ \begin {array}{ccc} -7&-12&13\\ 2&3&-5
\\ 2&3&-2\end {array} \right]
.$$
To find $A^{-1}$, we have to calculate $\det(A)$ which is given by
$$\det(A)=-3.$$
Finally, we have
$$A^{-1}=\frac{1}{\det(A)}\operatorname{adj}(A)=-\frac{1}{3}\left[ \begin {array}{ccc} -7&-12&13\\ 2&3&-5
\\ 2&3&-2\end {array} \right].$$
