Just for the record @amWhy, I don't think that this post is exactly a duplicate of the one you linked; they are definitely related, but the newer question is hung up on solving a system of linear equations
now, if there is a more canonical answer to "how do I solve a system of linear equations?" I am all for closing the question
I'm not quite sure what to make of this answer. It barely sketches the idea of a proof, and one of the three references cited appears to be the work of the answerer.
@XanderHenderson To me it's no better than a link only answer. The answerer states what they expect the OP to accept as fact, with no support as to why the statement holds.