I'm looking for some help with my intuition of basic matrix operations, specifically finding a matrix's inverse (as per my subject line). I have no problems with the steps. The basic row operations are relatively simple. I'd like to understand why/ how this solves the system of linear equations.
I know my question is asking more (or arguably less) than a concrete sequence of steps, a theorem, etc. But I think someone who understands linear algebra much better than I can get through to me better than my texts' treatment, which is little more than a worked example.
Thanks in advance..