1. The problem statement, all variables and given/known data Prove that a0 = 0 2. Relevant equations 3. The attempt at a solution Let V be a vector space on a field F. Let x be a member of V and a be a member of F. Consider that the 0 vector is the unique vector such that x + 0 = x Now, apply a scalar multiplication by a to both sides of the equation. Because scalar multiplication is distributive in all vector spaces, ax + a0 = ax Thus, we see that a0 has the same property of the 0 vector in V. Since the 0 vector in V is also unique, it must be the case that a0 = 0 QED Can I do that?