Question

Find the value of determinant $\left|\begin{array}{cc}5& -3\\ -7& -4\end{array}\right|$

Answer 1

$\left|A\right|=\left|\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right)\right|=a_{11}{a}_{22}-a_{21}{a}_{12}$

$|\begin{array}{cc}5& -3\\ -7& 4\end{array}-|=(5\ast -4)-(-7\ast -3)=-20-14=-34$