I have two square matrices $X$ and $Y$ of the order of $n \times n$. It is given that $X = I - XY$. I have to show that $X$ is invertible and that $XY = YX$.
The first part is fairly easy, moving stuff around gets me to the point that $X(I + Y) = I$ and therefore $X$ multiplied by another matrix yields the identity matrix and therefore $X$ is Invertible.
I am stuck at the second part which requires showing that $XY = YX$.
I tried multiplying $(I-XY)B$ but it got me nowhere.