Does the zero product property hold in vector spaces? – math.stackexchange.com

Does the zero product property hold in vector spaces? – math.stackexchange.com

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Suppose $V$ is a vector space over a field $F$. Let $v \in V\setminus \{0\}$ and $\lambda \in F$. Does $\lambda v= 0$ imply $\lambda = 0$?

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