What do you mean that an operation is commutative?

It means that when you exchange the two operands, the result doesn't change.

Example 1: For any two real numbers, a + b = b + a. In the real numbes, addition is commutative.

Example 2: For any two real numbers, ab = ba. In the real numbers, multiplication is commutative.

Example 3: For square matrixes, AB is not the same as BA. Multiplication of matrixes is NOT commutative.

Example 4: For vectors, a x b = - b x a. The cross product of vectors is NOT commutative.