sparsity

A bunch of matricies could be sparse; for fluid dynamics, for instance, has a 10^{6} \times 10^{6} matrix, but may only have 7 \times 10^{6} non-zero entries; but the inverse could be fully dense!
In these cases, we almost never want to form a in inverse if needed.
If we really need to invert this, performing a LU-Factorization is going to be a very good idea.