Dihedral groups are ambivalent

Statement
The dihedral group $$D_{2n}$$ is an ambivalent group: every element is conjugate to its inverse. Note that this also holds for the infinite dihedral group.

For finite dihedral groups, this implies that all irreducible characters (and hence, all characters) are real-valued.

Related facts

 * Generalized dihedral groups are ambivalent
 * Dicyclic groups of even degree are ambivalent