Vector space/Simple properties/Fact/Proof/Exercise

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

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

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