Simple homomorphism Question: Prove that $φ(s)$ is a reflection

Question

Let r ∈ D20 be an element of order 20 and let s ∈ D20 be a reflection. Suppose that φ : D20 → D20 is a homomorphism such that φ(r) = r^12

Prove that $φ(s)$ is a reflection

Answer 1

Since $s^2=1$ we have $\phi(s)^2=\phi(s^2)=\phi(1)=1$. Hence $\phi(s)$ is a reflection (possibly the trivial one).