Okay, the basic answer is that it is not a power of a prime. But that is a more advanced answer.

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.