1. The problem statement, all variables and given/known data a. In each case a binary operation * is given on a set M. Decide whether it is commutative or associative, whether an identity exists, and find the units. M=N(natrual); m*n = max(m,n) b. If M is a moniod and u in M, let sigma: M -> M be defined by sigma(a) = ua for all a in M. (a) show that sigma is a bijection if and only if u is a unit. (b) If u is a unit, describe the inverse mapping sigma^-1: M -> M 2. Relevant equations 3. The attempt at a solution In a, I know it is commutative and associative. I'm not sure identity and unit. max(m,0) = always m, so 0 is identity, right?? how about unit? 0 is also unit? in b, if u is a unit, sigma (a) = ua is gonne be identity or a??? Actually, I'm confusing about the concept of unit. Thanks.