  We present a solution to the sign problem in dynamical random matrix
simulations of a two-matrix model at nonzero chemical potential. The sign
problem, caused by the complex fermion determinants, is solved by gathering the
matrices into subsets, whose sums of determinants are real and positive even
though their cardinality only grows linearly with the matrix size. A detailed
proof of this positivity theorem is given for an arbitrary number of fermion
flavors. We performed importance sampling Monte Carlo simulations to compute
the chiral condensate and the quark number density for varying chemical
potential and volume. The statistical errors on the results only show a mild
dependence on the matrix size and chemical potential, which confirms the
absence of sign problem in the subset method. This strongly contrasts with the
exponential growth of the statistical error in standard reweighting methods,
which was also analyzed quantitatively using the subset method. Finally, we
show how the method elegantly resolves the Silver Blaze puzzle in the
microscopic limit of the matrix model, where it is equivalent to QCD.
