The question is: Suppose one has n×n square matrices X, Y and Z such that XY = I and Y Z = I. Show that it follows that X = Z. Now if this were XY and ZY, I would just say that: XY=ZY -> XY-ZY=0 ->Y(X-Z)=0 -> X-Z=0 -> X=Z. I am wondering that since the Y is on different sides of the Z and X this still holds? Thanks!