Mathematics - Matrix Question with Solution | TestHub

Given, $A=\left[\begin{array}{ccc}3& -2& 4\\ 1& 2& -1\\ 0& 1& 1\end{array}\right]$ and $A^{-1}=\frac{1}{k}\mathrm{adj}(A)$....(i) We know that, $A^{-1}=\frac{\mathrm{adj}(A)}{|A|}$...(ii) By comparing Eqs. (i) and (iii), $k=|A|$ So, $\begin{array}{rl}|A|& =\left|\begin{array}{ccc}3& -2& 4\\ 1& 2& -1\\ 0& 1& 1\end{array}\right|\\ & =3(2+1)+2(1+0)+4(1-0)=15\end{array}$