The fact that 2 · 3 gives the same result as 3 · 2, or 3 + 2 equals 2 + 3, is a special case of commutativity.
Definition
a * b = b * a
A binary operation * : V × V -> V is
called commutative if, for all a, b
V,
If the multiplication of a monoid or semi-group is commutative, then the monoid or semi-group itself is also called commutative.