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-Wooi-Chen | -Wooi-Chen | ||
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| + | I think if you prove its cyclic the inverse will always be the same | ||
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| + | -Matt | ||
Revision as of 11:43, 17 September 2008
How do you prove that an element and its inverse have the same order? I understand the idea but do not know how to prove it.
-Wooi-Chen
I thought this worked as a proof.
$ g^k=1 $ element g having order of k
$ (g^k)^{-1}=(1)^{-1} $
$ g^{-k}=1 $
$ (g^{-1})^k=1 $ inverse of g having order of k
This could be wrong, but it makes sense.
-Daniel
That actually makes sense to me as well. It is kind of playing with the order which power comes, that's the idea I get.
-Wooi-Chen
I think if you prove its cyclic the inverse will always be the same
-Matt
