  A class of background independent matrix models is made for which the
structure of both local gauge symmetries and classical solutions is clarified.
These matrix models do not involve a space-time metric and provide the matrix
analogs of topological Chern-Simons and BF theories. It is explicitly shown
that the BF type of matrix model can be formulated in any space-time dimension
and include 3+1 dimensional gravity as a special case. Moreover, we discuss
some generalization of the model to include a fermionic BRST-like symmetry
whose partition function is related to the Casson invariant.
