  Multi-loop calculations of the effective action for the matrix model are
important for carrying out tests of the conjectured relationship of the matrix
model to the low energy description of M-theory. In particular, comparison with
N-graviton scattering amplitudes in eleven-dimensional supergravity requires
the calculation of the effective action for the matrix model with gauge group
SU(N). A framework for carrying out such calculations at two loops is
established in this paper. The two-loop effective action is explicitly computed
for a background corresponding to the scattering of a single D0-brane from a
stack of N-1 D0-branes, and the results are shown to agree with known results
in the case N=2.
