General linear group/Injective group homomorphism for n \leq m/Exercise

Let ${}K$ be a field, and let ${}n,m\in \mathbb {N} _{+}$ with ${}n\leq m$. Define an injective group homomorphism

$\operatorname {GL} _{n}\!{\left(K\right)}\longrightarrow \operatorname {GL} _{m}\!{\left(K\right)}.$

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