Cayley Table for Commutative Operation is Symmetrical about Main Diagonal

Definition
Let $\left({S, \circ}\right)$ be an algebraic structure.

Then:
 * the Cayley table for $\left({S, \circ}\right)$ is symmetrical about the main diagonal


 * $\circ$ is a commutative operation.
 * $\circ$ is a commutative operation.