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Math Help - the inverse of a matrix

  1. #1
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    the inverse of a matrix

    Is the inverse of a matrix unique??

    If yes how do we prove that ?
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  2. #2
    Super Member Random Variable's Avatar
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    Assume that a nonsingular matrix has two inverse matrices and then show that the two matrices are equal to each other.
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  3. #3
    Super Member Gamma's Avatar
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    The same proof to show inverses in a group are unique works.

    Let A_1^{-1} and A_2^{-1} be inverses of A.
    A_1^{-1}=A_1^{-1}I_n=A_1^{-1}(AA_2^{-1})=(A_1^{-1}A)A_2^{-1}=I_nA_2^{-1}=A_2^{-1}
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