\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(A_1, \dots, A_k \in \mathbb{K}[X]^*\). Show that \(A_1 \wedge \dots \wedge A_k = 1\) iff there exist \(U_1, \dots, U_k \in \mathbb{K}[X]\) such that \(A_1 U_1 + \dots + A_k U_k = 1\).
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