By you can do it by checking whether it is a field or not.
The set is,
It froms a group under addition.
Furthermore, it is a ring (just check the definitions for a ring).
Furthermore, it is a commutative ring.
Furthermore, it has unity (1).
Thus, it is a commutative ring with unity.
Now, if every non-zero element has an inverse the proof is complete.
Thus, we need to show every element has a multiplicative inverse.
The element 2, has no inverse!
Just check each one and convince thyself.