non-zero Vector space with new scalar multiplication defined over finite field still vector space?

Question

If $V$ is a vector space (not the zero vector space) over $\mathbb{R}$, and if $F$ is a finite field. how could I show that it is not possible to define a new scalar multiplication of $F$ on $V$, in a way that $V$ with this scalar multiplication and the usual addition becomes a vector space over $F$?

Thanks in advance.