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

Suppose that a set G has a binary operation on it that has the following 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 that the right inverse of each element is a left inverse and that the right identity is also a left identity. See how many proofs you can give.

Expert Solution

Colby Messinger answered 2 years ago

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