Let G be a nonempty set equipped with an associative operation with these properties: (i) There is an element e of G such that ea=a for every a that's an element of G. (ii) For each a that's an element of G, there exists d that's an element of G such that da=e.   Prove that G is a group.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 27E: 27. Suppose that is a nonempty set that is closed under an associative binary operation and that...
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Let G be a nonempty set equipped with an associative operation with these properties:

(i) There is an element e of G such that ea=a for every a that's an element of G.

(ii) For each a that's an element of G, there exists d that's an element of G such that da=e.

 

Prove that G is a group.

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