Question: (a) We have seen that D 3 , the group of symmetries of the equilateral triangle, is not abelian. Show that for n > 2,

(a) We have seen that D₃, the group of symmetries of the equilateral triangle, is not abelian. Show that for n > 2, the dihedral group D_n is not abelian.

(b) Find all elements a of the group D₈ that commute with every element of D₈, i.e., find {a D₈: ax = xa for all x D₈}. Is this set a subgroup of D₈?

Please give explaination, thanks.

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