No, symbolic computation like that often takes a long long time; it becomes completely impractical with even fairly moderately sized matrixes (e.g, 35 x 35 is much too much.)
You can really only make improvements in the computation if M is (truly) sparse, or if M has special properties such as being tri-diagonal. The inverse of a sparse symbolic matrix is generally dense, but the length of the expressions get cut way way down if there are a lot of 0s.
