Question

If the sum of the elements of inverse of the matrix $\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]$ is $m$.Find $m$

Answer 1

$A=\left[\begin{array}{cc}-3& 2\\ 5& -3\end{array}\right]$

co factor matrix $=\left[\begin{array}{cc}-3& -5\\ -2& -3\end{array}\right]$

Adjoint matrix $=\left[\begin{array}{cc}-3& -2\\ -5& -3\end{array}\right]$

determinant $=(-3)(-3)-2\times 5$

$9-10=-1$

$\therefore A^{-1}=\left(\frac{AdjA}{|A|}\right)=\left[\begin{array}{cc}3& 5\\ 2& 3\end{array}\right]$

$\therefore m=$ sum of elements $=3+5+2+3$

$=13$