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Math Help - Indicate how A^-1 exists

  1. #1
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    Indicate how A^-1 exists

    Any help is appreciated!
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  2. #2
    Newbie eigenvex's Avatar
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    You can use determinants to prove it. You know if det(A) = 0, an inverse does NOT exist. So if you take det() of each side:

    det(2AB - 3AC) = det(I)

    det(A)*(det(2B - 3C)) = 1

    Can only be true if det(A) is nonzero, so the inverse must exist.

    Oh, and to get the second part, multiply both sides by A inverse.
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  3. #3
    MHF Contributor

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    You are given that 2AB+ 3AC= I. Write that as A(2B+ 3C)= I. Now, what is the definition of "inverse"?
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