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Homework Help: Matrix Multiplication Question

  1. Sep 26, 2007 #1
    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!
  2. jcsd
  3. Sep 26, 2007 #2
    I am sure you would have better luck in the math forums.

  4. Sep 26, 2007 #3

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    You are throwing away a lot of information in going from XY=1 and ZY=1 to XY=ZY. If Y is singular, there are infinitely many distinct matrices X and Z for which XY=ZY. With matrices and vectors, the step (X-Z)Y = 0 to X-Z=0 is in general invalid.

    Hint: What is XYZ?
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