1) The operation laws including:commutative law , associative law , cancellation law , unity of operation, inverse element, and distributive law between two operations, here we just omit them.

2) The commutative law holds for superposition without exception, but it does not necessarily for accumulation.

3) Generally the arithmetic of the matrix multiplication unconformity commutative law, but under special conditions they are interchangeable.

4) We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.

5) As a branch of modern algebra , finite fields is an abstract system in algebra which satisfies operational laws such as associative law, commutative law, distributive law etc.

6) Heisenberg had not proceeded very far with this idea before he noticed that it would lead to his physical quantities not satisfying the commutative law of multiplication.