3. Exercise 6.2. 6.20 Prove strictly from the axioms for a vector space the following four theorems. Each step in your proof must explicitly follow from one of the vector

space axioms or from a property of scalars or from a previously proved theorem. (a) The vector O is unique. [Assume that there are two, O1 and O2. Show that they're equal. First step: use axiom 4.] (b) The number 0 times any vector is the zero vector: 0v =0. (c) The vector v' is unique. \text { (d) }(-1) \vec{v}=\vec{v}^{\prime}