Commutative Property

Definition : Let $G$ be a set and $*$ be a binary relation. $*$ is commutative if for any $a,b \in G$ then $a*b = b*a$.

An example of this is in the real numbers. $2*3 = 3*2 = 6$. However this is not true when it comes to matrix multiplication since $A*B \neq B*A$ in some cases. This means that multiplication in real numbers is commutative but multiplication on matrices is noncommutative.