Exercise 2, § 1

Let $P = \{ z \in \mathbf{C} | \mathscr{J}(z) > 0 \}$. Let G be the group of bijections $z \mapsto az + b$ of P ($a > 0, b \in \mathbf{R}$). Then G operates on P simply transitively, which allows us to transport the complex analytic manifold structure on P to G. Show that the structure obtained is invariant under left translations of G but not under right translations.