The exercise:
Solve the system of matricial equations $MAX+NY=M$
$NAX+PY=N$
I am trying to determine $X$ and $Y$, but I know I can't use something like $M^{-1}$ or $N^{-1}$ because I don't know if the matrices are invertible. I think I have to somehow isolate one variable in one equation and substitute it on the other, but I was not able to find any content explaining exercises like this one.