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Thread: similar matrices

  1. #1
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    Mar 2008
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    similar matrices

    Let $\displaystyle A, B$ be square matrices of order $\displaystyle n$.
    If $\displaystyle A$ or $\displaystyle B$ is invertible, show that $\displaystyle AB$ is similar to $\displaystyle AB$.

    First I saw this question, I think there' s a typo in this question since every matrix is similar to itself.
    May be it should be $\displaystyle AB$ similar to $\displaystyle BA$.

    Anyway, i still can't solve it if it is $\displaystyle BA$.
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  2. #2
    Junior Member
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    Think about what you know.
    You know that A has an inverse (or similarly for B).
    So $\displaystyle A^{-1}$ exists. So chances are it's going to be very closely related to your similarity transformation.
    Hope that helps.
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