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Math Help - prove

  1. #1
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    Unhappy prove

    Assume that alpha:S-T, and beta: T-U, gamma: T-U. prove each of the following statements

    A) If alpha and beta are invertible, then beta of alpha is invertible.
    Last edited by mandy123; September 7th 2008 at 11:17 AM.
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  2. #2
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    Quote Originally Posted by mandy123 View Post
    Assume that alpha:S-T, and beta: T-U, gamma: T-U. prove each of the following statements

    A) If alpha and beta are invertible, then beta of alpha is invertible.
    I do the first one.
    A function is invertible if and only if it is one-to-one.
    Say \beta (\alpha (x) ) = \beta(\alpha(y)) \implies \alpha(x) = \alpha(y) \implies x=y.
    Thus, \beta \circ \alpha is invertible.
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