(a) Show that if

Is a 2 × 2 diagonal matrix with α ‰  b, then the only matrices that commute (under matrix multiplication) with D are other 2 × 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 × n diagonal matrix D with all distinct diagonal entries if and only if A is a diagonal matrix.

p-(1 0) 0b0 0