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Math Help - Prove that in a group

  1. #1
    Junior Member universalsandbox's Avatar
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    Prove that in a group

    (xy)^(-1) = b^(-1)a^(-1),

    keeping in mind the group may not be commutative. Thanks.
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  2. #2
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    Quote Originally Posted by universalsandbox View Post
    (xy)^(-1) = b^(-1)a^(-1),

    keeping in mind the group may not be commutative. Thanks.
    To show (ab)^{-1} = b^{-1}a^{-1} you need to show (ab)(b^{-1}a^{-1}) = e.
    Can you do that now?
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  3. #3
    Junior Member universalsandbox's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    To show (ab)^{-1} = b^{-1}a^{-1} you need to show (ab)(b^{-1}a^{-1}) = e.
    Can you do that now?
    Could you add a little more process to that please? This stuff is very new to me. Thanks.
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  4. #4
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    Quote Originally Posted by universalsandbox View Post
    Could you add a little more process to that please? This stuff is very new to me. Thanks.
    Say that x^{-1} = y. What does that mean? It means that xy = e and yx=e. That is the definition of what it means to be a multiplicative inverse. In your problem you have x=ab and y=b^{-1}a^{-1}.
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