1. The problem statement, all variables and given/known data Let S be a set with an operation * which assigns an element a*b of S for any a,b in S. Let us assume that the following two rules hold: 1. If a, b are any objects in S, then a*b = a 2. If a, b are any objects in S, then a*b = b*a (Herstein, Abstract Algebra, 2ed) 2. Relevant equations Is it safe to assume that the symmetry, transitivity, and reflexibility hold? 3. The attempt at a solution a = a*b = b*a = b But I am not sure if this is sufficient as it is my first course (in fact, first problem!) in abstract algebra... [Edit] Or with the relation obtained from the axioms of S, shall I proceed with proof by contradiction?