The matrix A has x rows and x+5 columns. The matrix B has y rows...

Given, Matrix A has $x$ rows and $x+5$ columns Matrix B has y rows and $11-$ y columns. Also given AB and BA exists. If A B$exists, then the number of rows in A$ most be equal to number of columns in $B$. i.e., $x=11-y\ldots(1) If BA exists, then$ the $number of rows in B must be equal to number of rows in A.$$\begin{aligned} & \text{ i.e., } x+5=y \\ & \Rightarrow 11-y+5=y(\text{ from }(1)) \\ & \Rightarrow 2 y=16\end{aligned}$$\text{ (1) } \Rightarrow x=11-8=3 \text{. } So,$x=3, y=8$.$