1. The problem statement, all variables and given/known data Let |v> ∈ V with |v> ≠ |0>, and let λ, μ ∈ ℂ. Prove that if λ|v> = μ|v>, then λ = μ 2. Relevant equations Vector Space Axioms 3. The attempt at a solution I am struggling to begin with this one. I can think of tons of different ways to begin, but all seem to get into a hazy area where I am unsure. I could start by adding or "subtracting" from both sides λ|v> or by adding 0 to both sides, or any other traditional proof ways. Is there any hint to help me go in the right direction?