Show that if $\displaystyle V $ is a set with 8 elements, then no matter how we define addition on $\displaystyle V$

and multiplication by scalars from $\displaystyle Z_3$, $\displaystyle V $ cannot be made a vector space over $\displaystyle Z_3$.

I'm thinking that I demonstrate that one of the properties of vector spaces, (closure, commutative etc) doesn't hold.

How do I show this for all different ways of defining addition and scalar multiplication though?