Vector space/Simple properties/Fact/Proof/Exercise

Let ${\displaystyle {}K}$ be a field, and let ${\displaystyle {}V}$ be a ${\displaystyle {}K}$-vector space. Show that the following properties hold (for ${\displaystyle {}v\in V}$ and ${\displaystyle {}s\in K}$).

1. We have ${\displaystyle {}0v=0}$.
2. We have ${\displaystyle {}s0=0}$.
3. We have ${\displaystyle {}(-1)v=-v}$.
4. If ${\displaystyle {}s\neq 0}$ and ${\displaystyle {}v\neq 0}$, then ${\displaystyle {}sv\neq 0}$.