VTRMC 2013 Problem 6

Let \begin{align*}X&=\begin{pmatrix}7&8&98&-9&-7-7&-7&9\end{pmatrix}Y&=\begin{pmatrix}9&8&-98&-7&77&9&8\end{pmatrix}.\end{align*}Let $A=Y^{-1}X$ and let $B$ be the inverse of $X^{-1}+A^{-1}$ . Find a matrix $M$ such that $M^2=XY-BY$ (you may assume that $A$ and $X^{-1}+A^{-1}$ are invertible).