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?