  We study a matrix model with a cubic term, which incorporates both the fuzzy
S^2*S^2 and the fuzzy S^2 as classical solutions. Both of the solutions decay
into the vacuum of the pure Yang-Mills model (even in the large-N limit) when
the coefficient of the cubic term is smaller than a critical value, but the
large-N behavior of the critical point is different for the two solutions. The
results above the critical point are nicely reproduced by the all order
calculations in perturbation theory. By comparing the free energy, we find that
the true vacuum is given either by the fuzzy S^2 or by the ``pure Yang-Mills
vacuum'' depending on the coupling constant. In Monte Carlo simulation we do
observe a decay of the fuzzy S^2*S^2 into the fuzzy S^2 at moderate N, but the
decay probability seems to be suppressed at large N. The above results,
together with our previous results for the fuzzy CP^2, reveal certain
universality in the large-N dynamics of four-dimensional fuzzy manifolds
realized in a matrix model with a cubic term.
