Suppose $A,B\in M_{n}(\Bbb C)$ satisfies for $\forall a,b\in \Bbb C,aA+bB$ is always diagonalizable.
Show that $$AB=BA.$$
2026-04-03 07:33:50.1775201630
How prove this linear algebra $AB=BA$?
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It's a non trivial result. It has indeed be the object of papers: