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Thread: inverse proof

  1. #1
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    inverse proof

    hello
    here is a proof that i could not do anything to it

    If $\displaystyle A$ and $\displaystyle B$ are two nn nonsingular matricesm, prove that $\displaystyle B^TA^{-1}$ is nonsingular and $\displaystyle (B^TA^{-1})^{-1}=A(B^{-1})^T$

    I want a start
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  2. #2
    MHF Contributor

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    First, can you prove that if A is non-singular, the $\displaystyle A^T$ is non-singular and $\displaystyle (A^T)^{-1}= (A^{-1})^T$. (Use the definition of "$\displaystyle A^T$".
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