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Thread: a question on invertible matrices

  1. #1
    Junior Member
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    a question on invertible matrices

    suppose A and B are invertible matrices.
    Show that Bt is also invertible by producing a matrix C such that (BtA)C=I and C(BtA)=I

    thanks


    Mr F edit: The OP adds that t is the transpose. So the question is probably the following:

    Suppose A and B are invertible matrices.
    Show that $\displaystyle B^T$ is also invertible by producing a matrix C such that $\displaystyle (B^T A) C = I$ and $\displaystyle C (B^T A) = I$.
    Last edited by mr fantastic; Mar 27th 2009 at 04:02 AM.
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  2. #2
    MHF Contributor

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    If B has an inverse, so does $\displaystyle B^T$. What is $\displaystyle (B^TA)(A^{-1}(B^T)^{-1})$ and $\displaystyle (A^{-1}(B^T)^{-1})(B^TA)$?
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