Two very nice (& free) CAS packages:
Maxima (or wxMaxima) (free Mathematica/Maple competitor): http://maxima.sourceforge.net/
Smath (free Mathcad clone): http://en.smath.info/
Haven't used Smath in a long time, but wxMaxima is pretty darn good. Smath/Mathcad historically handles units rather...
For small order matrices you mention the free and pretty darn good Maxima would likely suffice. A bit of a learning curve, but not worse than Maple/Mathematica.
http://maxima.sourceforge.net/