HEY to everyone, never posted here before!!
if given 2v = v, would it be correct, to prove v = 0, by doing the following, (using the axioms of scalar multiplication and addition for a k-vector space)
v = v + (v - v) = (v + v) - v = 2v - v, so
as 2v=v then
2v-v = v-v = 0.
thanl u in advance for ur help!