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Groups : Indentities and Inverses

If G is a group, then

(1) the identity element of G is unique,
(2) every a belongs to G has a unique inverse in G.

Solution Preview


(1) Suppose that e and e' are both identity elements in G. Then, by group property (2), we have

ea= a , for every a in G.

In particular, ee' = ...

Solution Summary

Indentities and inverses are discussed.