Question Number 175266 by oustmuchiya@gmail.com last updated on 25/Aug/22
$$\mathrm{Find}\:\mathrm{matrix}\:\mid\mathrm{A}\mid\mathrm{A}^{-\mathrm{1}} \: \\ $$$$\mathrm{given}\:\mathrm{that}\:\mathrm{matrix}\: \\ $$$$\mathrm{A}=\begin{pmatrix}{\sqrt{\mathrm{2}}}&{-\mathrm{1}}&{\mathrm{1}}&{\:\mathrm{0}}\\{\mathrm{4}}&{\mathrm{3}}&{\mathrm{2}}&{-\mathrm{1}}\\{\mathrm{0}}&{\mathrm{2}}&{\mathrm{3}}&{\:\mathrm{1}}\\{\mathrm{1}}&{-\mathrm{1}}&{\mathrm{0}}&{\:\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{using}\:\mathrm{row}\:\mathrm{operations} \\ $$
Commented by kaivan.ahmadi last updated on 27/Aug/22
$${easy} \\ $$$$\mid{A}\mid.{A}^{−\mathrm{1}} =\mid{A}\mid.\frac{\mathrm{1}}{\mid{A}\mid}{A}^{\ast} ={A}^{\ast} ={A}_{{ij}} ^{{T}} \\ $$$$ \\ $$