Of course $\displaystyle r\not = r^{-1}$ because that would imply $\displaystyle \text{ord}(r) = 1 \text{ or }2$ which we know is impossible since $\displaystyle \text{ord}(r) = k>2$ (Here we are assuming the dihedral group is sufficiently large). Thus, this shows that neither of these two elements commutes.