Chapter 3.1, Problem 37P

If $\det \left(A\right)\ne 0$, derive the result in Eq. $\left(14\right)$ for $A^{-1}$.

$A^{-1}=\frac{1}{\det \left(A\right)}\left(\begin{array}{cc}{a}_{22}& -a_{12}\\ -a_{21}& a_{11}\end{array}\right)$ … (14)