Answer
$|A|=-10$ and $|A^{-1}|=-\frac{1}{10}$.
Work Step by Step
Let $A$ be given by $$A=\left[ \begin {array}{ccc} 1&0&1\\ 2&-1&4
\\ 2&6&0\end {array} \right]
,$$
then we have $A^{-1}=\left[ \begin {array}{ccc} {\frac {12}{5}}&-\frac{3}{5}&-\frac{1}{10}
\\ -\frac{4}{5}&\frac{1}{5}&\frac{1}{5}\\ -\frac{7}{5}&\frac{3}{5}&\frac{1}{10}
\end {array} \right]
$.
Now, $|A|=-10$ and $|A^{-1}|=-\frac{1}{10}$. Hence, we verify that
$$|A^{-1}=\frac{1}{|A|}.$$
