(a) Show that if Is a 2 à 2 diagonal matrix with α b, then the only...
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Is a 2 à 2 diagonal matrix with α b, then the only matrices that commute (under matrix multiplication) with D are other 2 à 2 diagonal matrices.
(b) What if a = b?
(c) Find all matrices that commute with
where a, b,c are all different.
(d) Answer the same question for the case when a b = c.
(e) Prove that a matrix A commutes with an n à n diagonal matrix D with all distinct diagonal entries if and only if A is a diagonal matrix.
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