Groups : Indentities and Inverses
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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.
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Solution Summary
Identities and inverses are discussed. The expert identifies the elements of G for a group.
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Proof:
(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' = ...
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