1. A2 and M2 are the associative laws of addition and multiplication respectively.

2. This paper offers two methods to verify the associative law.

3. 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.

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. Here we have used the associative law or the cancellation law for multiplication, which are satisfied for natural numbers, now we assume they are satisfied with fraction numbers.

6. A new multiplication of the cubic matrices is given, and testified the associative law and the distributive law of the new multiplication are right under the new multiplication.

7. 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.