(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Prove the following is a group

**Physics Forums | Science Articles, Homework Help, Discussion**