how do you prove that if V is a vector space andvis a vector and c is any scalar, then if cv=0, it means that c=0 orv=0?

i was thinking of using the fact that sincevis in V, there exist a negative vector-vin V.

so cv+ (-cv) = c (v+ (-1)v) =c0= 0

then after that, im not sure how im going to show that c=0 orv=0..