| Line 11: | Line 11: | ||
<math>(g^k)^{-1}=(1)^{-1}</math> | <math>(g^k)^{-1}=(1)^{-1}</math> | ||
| − | <math>g^-k=1</math> | + | <math>g^{-k}=1</math> |
<math>(g^{-1})^k=1</math> inverse of g having order of k | <math>(g^{-1})^k=1</math> inverse of g having order of k | ||
Revision as of 17:24, 16 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
