Answer
(a) $|A|=-31.$
(b) $|A^{-1}|= -\frac{1}{31}.$
Work Step by Step
Since $$A=\left[ \begin {array}{cccc}2&-1&4\\ 5&0&3\\1&-2&0
\end {array} \right]=\left[ \begin {array}{cccc}2&-1&4\\ 5&0&3\\-3&0&-8
\end {array} \right],$$
we have
(a) $|A|=-31.$
(b) $|A^{-1}|=|A|^{-1}=-\frac{1}{31}.$
