# Vektorraum/Einfache Eigenschaften/Fakt/Beweis/Aufgabe/en

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

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