Proving Dn Non-Abelian for n >= 3

[zcdfhn]

My goal is to prove that if n >= 3 then D_n, which is the dihedral group of size n is non-abelian.

I am stuck, but my attempt at a solution was to show that some the symmetries in D_n are not commutative under composition, but I do not know how to prove that for n cases. My other attempt was to find a isomorphism to D_n and show that its isomorphism is not abelian, but I have no clue where to start from there.

I would appreciate either an answer, or something to help me get going. Please be precise and I thank you so much in advance.

 

[Dick]

In general, a rotation doesn't commute with a reflection.