VTRMC 1979 Problem 2

Let $S$ be a set which is closed under the binary operation $\circ$ , with the following properties: (i) there is an element $e \in S$ such that $a \circ e = e \circ a = a$ , for each $a \in S$ . (ii) $(a \circ b) \circ (c \circ d)=(a \circ c) \circ (b \circ d)$ , for all $a,b, c,d \in S$ .

Prove or disprove: (a) $\circ$ is associative on S (b) $\circ$ is commutative on S