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Math Help - Inverse Isometry Proof Hint Help

  1. #1
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    Smile Inverse Isometry Proof Hint Help

    Hi I've been given the following exercise:

    Let FGH be the composite of three isometries. Assume that there inverses exist. Prove that (FGH)^-1 exists, and express this inverse in terms of the inverses of the individual isometries.

    I would greatly appreciate any hint about where to start and any general advice about attempting to solve problems of this sort. I need to rewire my brain, and I can't quite get it yet.

    Thanks,
    Ultros
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  2. #2
    Oli
    Oli is offline
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    Haven't really done isometry, but assuming it is a little like group theory...

    Presumably the inverse is

    H^-1G^-1F^-1...

    This exists since the inverse of F,G and H exists, and thus the composition exists.

    Prove that it is actually an inverse by sticking it before FGH and showing you get the identity element.
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