Answer to Question #18565 in Algebra for Irvin

Question

Let G be the dihedral group of order 2n generated by two elements r, s with relations rn = 1, s2 = 1 and srs^−1 = r^−1. Let θ = 2π/n.
For any integer h (0 ≤ h ≤ n), show that Dh(r) =
cos hθ −sin hθ
sin hθ cos hθ
Dh(s) =_
1 0
0 −1
defines a real representation of G.