Answer
(a) $|A|=-20.$
(b) $|A^{-1}|= -\frac{1}{20}.$
Work Step by Step
Since $$A=\left[ \begin {array}{cccc}1&0&-4\\ 0&3&2\\-2&7&6
\end {array} \right]=\left[ \begin {array}{cccc}1&0&-4\\ 0&3&2\\0&7&-2
\end {array} \right],$$
we have
(a) $|A|=-20.$
(b) $|A^{-1}|=|A|^{-1}=-\frac{1}{20}.$
