Putnam 1971 B1

B-1. Let $S$ be a set and let $\circ$ be a binary operation on $S$ satisfying the two laws $$\begin{array}{l} x \circ x=x \text { for all } x \text { in } S \text {, and } \\ (x \circ y) \circ z=(y \circ z) \circ x \text { for all } x, y, z \text { in } S . \end{array}$$

Show that $\circ$ is associative and commutative.