1. The problem statement, all variables and given/known data Let v ∈ V and c ∈ ℂ, with c ≠ 0. Prove that if cv = 0, then v = 0. 2. Relevant equations Vector space axioms. 3. The attempt at a solution Simple proof overall, but I have one major clarification question. v = 1v = (c^(-1)c)v = c^(-1) (cv) = c^(-1) 0 v = 0 My question is, in a complex vector space, is it safe to assume that c^(-1) exists in this proof? If it does, I feel very confident about this proof. If it doesn't then I need to do something else. I don't see anywhere in the vector space axioms that states the multiplicative inverse exists. But, it makes sense to me that an inverse does exist for any possible scalar choice here.