$ A^{-1}=\left[ \begin{array}{cc} 1&2\\ 1&3 \end{array} \right] $; $ B=\left[ \begin{array}{cc} 4\\ 6 \end{array} \right] $; $ X=\left[ \begin{array}{cc} x\\ y \end{array} \right] $
Solve $AX=B$. If $A^{-1}B^{-1}=C^{-1}$, find A.
I was able to solve for $X=A^{-1}B\rightarrow \left[ \begin{array}{cc} 16\\ 22 \end{array} \right] $
But I am unable to find A. Any help is much appreciated.
Find $A$ by taking the inverse of $A^{-1}$. $$A=(A^{-1})^{-1}=\left[ \begin{array}{cc} 3&-2\\ -1&1 \end{array} \right]$$