Answer
$$|A|=2, \quad \left|A^{-1}\right|=\frac{1}{2}.$$
Work Step by Step
Since $$A=\left[ \begin {array}{cccc} 0&1&0&3\\ 1&-2&-3&1
\\ 0&0&2&-2\\ 1&-2&-4&1
\end {array} \right]
,$$
then we can find the inverse as follwos
$$A^{-1}=\left[ \begin {array}{cccc} 2&-3&\frac{7}{2}&4\\ 1&-3&\frac{3}{2}&3
\\ 0&1&0&-1\\ 0&1&-\frac{1}{2}&-1
\end {array} \right] .
$$
One can see that
$$|A|=2, \quad \left|A^{-1}\right|=\frac{1}{2}.$$
Hence, we verify that $$\left|A^{-1}\right|=\frac{1}{|A|}.$$
