  We investigate the spectral properties of a random matrix model, which in the
large $N$ limit, embodies the essentials of the QCD partition function at low
energy. The exact spectral density and its pair correlation function are
derived for an arbitrary number of flavors and zero topological charge. Their
microscopic limit provide the master formulae for sum rules for the inverse
powers of the eigenvalues of the QCD Dirac operator as recently discussed by
Leutwyler and Smilga.
