So eg in this Khan Academy video Sal proves that A.T@A makes an invertible (non-singular) matrix.
But eg if A = [[1,2,3],[4,5,6],[7,8,9]], that's not the case? Why is that? What am I missing?
Additional question: I noticed if I do B = A.T@A and then C = B.T@B, then C is indeed invertible! Is that a coincidence or is there some mathematical basis for why double transpose works when singular doesn't?
Note: practitioner here, not mathematician, so apologies if this is stupid. Also would appreciate an answer without long proofs:)