Definition:Commutative

Let $$\circ$$ be a binary operation.

Two elements $$x, y$$ are said to commute (or permute) if $$x \circ y = y \circ x$$.

The binary operation $$\circ$$ is commutative on $$S$$ iff:

$$\forall x, y \in S: x \circ y = y \circ x$$