The general-purpose matrix inversion routine in Maxima is m^^-1. Invert
-- as documented -- is useful for certain special cases. It is also
documented that: "The current implementation is inefficient for matrices
of high order." The determinant command is also inefficient.
As for keeping your result in floating point, set keepfloat:true, e.g.
float(m)^^-1, keepfloat: true;
Please let us know if you have other problems.
-s