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The order of an elementg in a group is the least positive integer k such that gk is the identity.

Now look at the same group, we know there exists an element h such that gh=hg=e where e is the identity. This must be true because existence of inverses is one of the conditions required for a set to be a group. So if gk=e and gh=e, then gk =gh and we see the relation between k, the order and h the inverse in the group.

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Q: How Order of element is equal to its inverse in group?
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