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Math Help - Need some help with groups..

  1. #1
    Junior Member ginafara's Avatar
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    Need some help with groups..

    I can see that it is true, but not sure how to prove it...

    Problem:

    Let G be a group of order 3, and let, e,a,b, be the three elements of G, where e is the identity of the group. SHOW that b must be the inverse of a.

    TIA
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ginafara View Post
    I can see that it is true, but not sure how to prove it...

    Problem:

    Let G be a group of order 3, and let, e,a,b, be the three elements of G, where e is the identity of the group. SHOW that b must be the inverse of a.

    TIA
    G is closed and each of its elements are distinct so ab is equal to e, a, or b. Well ab = a \implies b = e and ab = b \implies a = e, so we are left with ab = e \implies a^{-1} = b. (Similarly for ba.)

    -Dan
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