Question

Prove S is a ring given s={1,2,3,4}

The addition Chart looked like this

+	1	2	3	4
1	2	3	4	1
2	3	4	1	2
3	4	1	2	3
4	1	2	3	4

The multiplication chart looked like this but i dont remember the middle numbers

X	1	2	3	4
1				4
2				4
3				4
4	4	4	4	4

This is a question i had on a test but cant remember what the numbers for the multiplication chart were. I know in order for it to be a ring in addittion it has to meet the following: n

1. be closed

2. associative

3. commutative

4. Identiy

5. Inverse

6. Distributive have to be true

and for multiplication only

1. and 2. have to be true but how do you prove this using the matrix? Can someone please explain. Thank you!!!

Answer 1