1. The problem statement, all variables and given/known data Suppose one has n×n square matrices X, Y and Z such that XY = 1and Y Z = 1. Show that it follows that X = Z. 3. The attempt at a solution Now I know if the equatoins had been XY and ZY I would do this: XY=ZY -> XY-ZY=0 -> Y(X-Z)=0 -> X-Z=0 -> X=Z I was wondering if this holds when the Y is on opposite sides of the other matrices? Thanks in advanced!