1) Could you please send us a copy of the matrix you are having trouble
inverting, and also your full configuration (processor type, OS version,
Lisp version, Maxima version)? That's really the only way to track down
problems like this. The problem may have nothing to do with matrix
inversion per se (though the fact that it fails when you float it does
suggest that that's where the problem is).
2) It is possible that there is a bug in Maxima's handling of sparse
matrix inversion. That is, in trying to be clever, it may be messing
up. To test this hypothesis in the floating case, try setting all the
zero elements to e.g. 1.0e-50.
3) Matrix operations in Maxima could probably be speeded up
considerably. Some simple tests show, for example, that determinant(m)
for a 12x12 dense integral m takes 10 times longer than m^^-1 (!!!).
-s