Need help to find my mistake in a simple proof of a matrix algebra proposition.

  1. 1. The problem statement, all variables and given/known data
    Is the following true for matrices?

    Hypotesis:
    AB = AC
    A != 0(zero matrix)

    Thesis:
    B=C

    3. The attempt at a solution

    AB = AC
    AB - AC = 0(zero matrix)
    AB - AC = A(B-C) // using the following property: A(B+C) = AB + AC iff A is mn matrix and BC are np matrices
    A(B-C) = 0 <=> B=C because A != 0
    QED

    There is something wrong because there are matrices where AB = AC and B != C.
    Where is my mistake?
     
  2. jcsd
  3. Dick

    Dick 25,626
    Science Advisor
    Homework Helper

    There are matrices where AB=0 and neither A nor B are zero. You can't say A(B-C)=0 implies A=0 or (B-C)=0 like you can with real numbers.
     
  4. ok, thanks
     
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