## Elementary Linear Algebra 7th Edition

(a) $|A|=-31.$ (b) $|A^{-1}|= -\frac{1}{31}.$
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) $|A^{-1}|=|A|^{-1}=-\frac{1}{31}.$