Note Set 05b: Inverting matrices using only a spork and row operations

At the edge of madness, we finally see that our comrade Ax=b can help us succeed through Gauss-Jordan elimination. Row operations allow us to travel out of the darkness, from $[\, \mathbf{A}\, |\, \mathbf{I}\, ]$ to $[\, \mathbf{I}\, |\, \mathbf{A}^{-1}\, ]$, with a full 2x2 example and the plan for 3x3s and up.
Best consumed by 2016/09/12