Determinant/Surjective group homomorphism to K^x/Exercise

Let ${}K$ be a field, and ${}n\in \mathbb {N} _{+}$. Show that the determinant

$\operatorname {GL} _{n}\!{\left(K\right)}\longrightarrow (K\setminus \{0\},\cdot ,1),M\longmapsto \det M,$

is a surjective group homomorphism.

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