Trace/V over K/Linearity/Exercise

Let ${}K$ be a field, and let ${}V$ be a finite-dimensional ${}K$-vector space. Show that the assignment

$\operatorname {End} _{}{\left(V\right)}\longrightarrow K,\varphi \longmapsto \operatorname {trace} {\left(\varphi \right)},$

is ${}K$-linear.

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