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Thread: Find A

  1. #1
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    Find A

    if AB =
    [1 1]
    [3 4] and $\displaystyle b^{-1} $=

    [1 -1]
    [1 2], find A


    I know it's a simple question, i am just not sure if

    $\displaystyle AB * B^{-1} = A $
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  2. #2
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    Quote Originally Posted by wopashui View Post
    if AB =
    [1 1]
    [3 4] and $\displaystyle b^{-1} $=

    [1 -1]
    [1 2], find A


    I know it's a simple question, i am just not sure if

    $\displaystyle AB * B^{-1} = A $

    Yes.

    Tonio
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  3. #3
    MHF Contributor

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    By the "associative law", $\displaystyle (AB)B^{-1}= A(BB^{-1})$. By the definition of "multiplicative inverse", $\displaystyle BB^{-1}= I$ and by the definition of "multiplicative identity", $\displaystyle AI= A$.
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