Question

Find the inverse of the matrix $A=$ $\left[\begin{array}{cc}2& -4\\ 3& -5\end{array}\right]$.

Answer 1

|A| = $\left|\begin{array}{cc}2& -4\\ 3& -5\end{array}\right|=-10+‘12=2\ne 0$
$\therefore A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]=\frac{1}{2}\left[\begin{array}{cc}-5& 4\\ -3& 2\end{array}\right]$
$\left[\begin{array}{cc}\frac{-5}{2}& 2\\ \frac{-3}{2}& 1\end{array}\right]$