Vector Space Properties: Show that the properties in Problems 1-3 hold in any vector space? 1. Unique

Question:

Vector Space Properties: Show that the properties in Problems 1-3 hold in any vector space?
1. Unique Zero: The zero element in a vector space is unique. Start with two zero elements and show that they must be equal.
2. Unique Negative: The negative of a vector is unique?
3. Zero as Multiplier: For any vector v̅, 0v̅ = 0̅?