Endomorphisms on vector space/Ring/Exercise

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

${}\operatorname {End} _{}{\left(V\right)}={\left\{\varphi :V\rightarrow V\mid \varphi {\text{ linear}}\right\}}\,$

is, with the natural addition and the composition of mappings, a ring.

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