  We show that integrability and symmetries of the near horizon geometry of the
D1-D5 system determine the S-matrix for the scattering of magnons with
polarizations in AdS3 $\times$ S3 completely up to a phase. Using
semi-classical methods we evaluate the phase to the leading and to the one-loop
approximation in the strong coupling expansion. We then show that the phase
obeys the unitarity constraint implied by the crossing relations to the
one-loop order. We also verify that the dispersion relation obeyed by these
magnons is one-loop exact at strong coupling which is consistent with their BPS
nature.
