(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that a nonempty set S with an associative binary operation * on S such that a*c=b and d*a=b have solutions in S for all a,b in S is a group.

2. Relevant equations

3. The attempt at a solution

In order to prove something is a group, I know that I must show associativity of *, existence of identity element and inverse for each element in S.

- We are given that S has an associative binary operation, so that is satisfied.

- In regards to finding the identity element such that a*e=e*a=a for all a in S...this is where I am not sure where to begin. Any suggestions on how to start?

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# Prove the following is a group

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