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Linear Algebra Similar Matrices Problem

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data

    Find two 2 × 2 matrices A and B such that AB fails to be similar to
    BA. Hint: it can be arranged that AB is zero but BA is not.


    2. Relevant equations

    N/A


    3. The attempt at a solution

    If AB similar to BA, AB = S-1BAS for some S, so AB DNE S-1BAS?
    Or maybe det(AB) DNE det(BA)
    I'm really not sure how to do this without guess and check, which I also tried and failed at
     
  2. jcsd
  3. Dec 8, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    You aren't paying much attention to the hint. If AB=0 and BA is not zero, then they aren't similar. Look for a example of that.
     
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