  We evaluate the effective actions of supersymmetric matrix models on fuzzy
S^2\times S^2 up to the two loop level. Remarkably it turns out to be a
consistent solution of IIB matrix model. Based on the power counting and SUSY
cancellation arguments, we can identify the 't Hooft coupling and large N
scaling behavior of the effective actions to all orders. In the large N limit,
the quantum corrections survive except in 2 dimensional limits. They are O(N)
and O(N^{4\over 3}) for 4 and 6 dimensional spaces respectively. We argue that
quantum effects single out 4 dimensionality among fuzzy homogeneous spaces.
