\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(A \in M_n(\mathbb{K})\) commute with every matrix \(M \in M_n(\mathbb{K})\). Show that \(A\) is a scalar matrix, i.e.\ \(A = \lambda I_n\) for some \(\lambda \in \mathbb{K}\).
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.