Programs to compute simple matrix operations; free for commercial use

[KingNothing]

Do any such programs exist?

[micromass]

You mean you're looking for a free program that can work with matrices??

Sure, that exists. Here is one: http://maxima.sourceforge.net/

[DaleSpam]

Python.

[Simon_Tyler]

I second DaleSpam, Python and NumPy (http://numpy.scipy.org/) is what you want. (Maxima is good with numerics, but is more known for its symbolics)

However, if you're used to something like matlab, then have a look at octave (http://www.gnu.org/software/octave/doc/interpreter/Introduction.html#Introduction).

Also, most programming languages have (free) libraries for array/matrix operations / linear algebra.
E.g. ATL or uBLAS are the standards for C++. Just google for more.