\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that if \(A \in \mathrm{GL}_n(\mathbb{K})\), then the homogeneous system \(A X = 0_{n,1}\) admits only the trivial solution \(X = 0_{n,1}\).
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