  The Matrix String Theory, i.e. the two dimensional U(N) SYM with N=(8,8)
supersymmetry, has classical BPS solutions that interpolate between an initial
and a final string configuration via a bordered Riemann surface. The Matrix
String Theory amplitudes around such a classical BPS background, in the strong
Yang--Mills coupling, are therefore candidates to be interpreted in a stringy
way as the transition amplitude between given initial and final string
configurations. In this paper we calculate these amplitudes and show that the
leading contribution is proportional to the factor g_s^{-\chi}, where \chi is
the Euler characteristic of the interpolating Riemann surface and g_s is the
string coupling. This is the factor one expects from perturbative string
interaction theory.
