- #1
ConeOfIce
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Homework Statement
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.
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!