Linear Algebra Similar Matrices Problem

  • Thread starter SuperZero
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  • #1
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Homework Statement



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.


Homework Equations



N/A


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
 

Answers and Replies

  • #2
Dick
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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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