1,2

1. S=QQ,Q is the set of rational numbers, * is a binary operator on S,a,b,x,yS,a,bx,y=ax, ay+b>. (1) Determine whether or not the operation * on S is commutative, associative, and idempotent? (2) Determine whether or not the operation * on S has identity and zero element? If it has, please list them, and further find the inverse element of every invertible element in S. - 2. Let S={a,b}, there are 4 operators on S : *, , ., and , as shown in the following table. - (1) Among the 4 operations, which of them are of commutativity, associativity, and idempotency? - (2) For every operator, find its identity, zero, and the inverse element of every invertible element