Tell whether or not with the two operations ⊕ and (in fact I want to type the but with a circle as in ⊕ but I don't know how to) is a field.

Looking to my class notes, a field is a set with 2 operations " " and " " such that

1)

2)

3) element " " such that

4) , such that

5)

6)

7) element such that

8) , such that

9) .

So to solve my problem, I have to check if any and elements of respect the 9 rules. But I'm not able to start. How can I check if any element and of are such that ? I thought about writing down and But it doesn't solve the problem. (Note that and ).

I also see that a field is a set with 3 elements as minimum. (unless , an can be the same element.)