On the course website [1], you can find currently three links
to IPython matrix computations using SymPy [2, 3, 4].
You can perform the same computations at SymPy Live [5].
For additional info about SymPy Matrix commands, see [6].

One difference: where I might have typed, say, "display(A)" 
alone on a line in [3, 4], just type "A" on a line. 
The display command makes the typesetting prettier, 
but is not essential; the SymPy plain-text output format 
is just like in [2], and is good enough.

[1] http://dkmj.org/b219ce022e0efd7bf329083baeb1cc6b/

[2] http://dkmj.org/b219ce022e0efd7bf329083baeb1cc6b/ipython/rref.html

[3] http://dkmj.org/b219ce022e0efd7bf329083baeb1cc6b/ipython/rref2.html

[4] http://dkmj.org/b219ce022e0efd7bf329083baeb1cc6b/ipython/kernels.html

[5] http://live.sympy.org/

[6] http://docs.sympy.org/0.7.2/modules/matrices/matrices.html