You can find the first chapter as a pdf download here: http://geometricalgebra.org/downloads/ga4cs_chapter1.pdf. It contains some code examples, and the complete source code is here: http://geometricalgebra.org/sandbox.html
The GACS book is indeed great. The “conformal model” defined there is very pleasant to work with. If you want to learn about it without buying a textbook, there’s also this PhD thesis: http://www2.eng.cam.ac.uk/~rjw57/pdf/r_wareham_pdh_thesis.pd...
Even more lightweight than matrices is just implementing the transformation on vector objects yourself: a 90-degree rotation left is R(x,y) = (-y, x), and (-R)(x,y) = -(R(x,y)). In higher dimensions this remains true for any 2-dimension subplane, so R_zx(x,y,z) = (z,y,-x).
Rotation matrices / other formulations become necessary when you're dealing with being able to rotate through any angle.
Though, doing rotations of the matrix 'y = Rx' form suffers mathematical problems like numerical instability and bad behavior. Quaternion rotations or Geometric Algebra's rotors (which are equivalent for N=3, and both take the form y = RxR^-1) work a lot better, and also eliminate a lot of the redundancy in the (skew-symmetric) rotation matrices formulation (4 variables instead of 9, for 3d).
It's easy to reach for complex numbers when they're built-in. Do you have to use Maple/Mathematica for this stuff, or can you do it easily in Python/JS/&c ?