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Suppose that a set G has a binary operation on it that has the following properties: 1....

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Advance Math

Suppose that a set G has a binary operation on it that has thefollowing properties:

1. The operation ? is associative, that is:

for all a,b,c ? G, a?(b?c)=(a?b)?c

2. There is a right identity, e:

For all a?G a?e=a

3. Every element has a right inverse:

For all a?G there is a^-1 such that a?a^-1=e

Prove that this operation makes G a group. You must show thatthe right inverse of each element is a left inverse and that theright identity is also a left identity. See how many proofs you cangive.

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