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Math Help - Simplifying matrices

  1. #1
    Senior Member
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    Simplifying matrices

    The question:
    Given that A, B and C are invertible n x n matrices, simplify

    A^2(B^{-1}CA)^{-1}B^{-1}C^T

    My attempt:
    First I expanded A^2 to AA:
    AA(B^{-1}CA)^{-1}B^{-1}C^T

    Then I found the inverse of the matricies within the parenthesis:

    AAA^{-1}C^{-1}BB^{-1}C^T

    AA^{-1} and BB^{-1} are just I (the identity matrix) and can be removed:

    AC^{-1}C^T

    Does this look correct? My text has no solution for this question. I'm trying to think if I can do something with the C matrices.

    Thanks!
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  2. #2
    A Plied Mathematician
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    Looks great! I don't think you can do anything more, unless you happen to know before-hand that C is unitary.
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  3. #3
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    Thanks for the quick reply.
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  4. #4
    A Plied Mathematician
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    You're welcome. Have a good one!
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