This is not the answer you are looking for, but an alternative module for dealing with matrices is the Perl Data Language. The module PDL::Slatec has a function called matinv , which is gives the inverse of a square matrix like so, ($inv) = matinv($mat) (pretty much stolen from the docs)

You will probably lose a little time installing and learning how to form the matrix, but if you are regularly involved in Numerical Funny Business, it might be worth it in the long run. The web page is http://pdl.perl.org/ which will explain the module and lead you to a low traffic mailing list with lotsa helpful people.