For a Science Fair I am trying to write a program that will a system (equation)
of 3 matrices of which only one is a square matrix:

[4 x 5] [5 x 4] = [4 x 4] Matrix
Inverses cannot be used. There is no inverse of non square matrices.
I may just settle for square matrices. Does anyone know a short algortihm
to calculate the determinant of a matrix? The inverse would be nice but
if it just the determinant that is fine.
If anyone know of Gauss[-Jordan] elimination algortihms for systems of equations
please say something. I would really appreciate.

Thanks,
Really Big Headache