Let A and B be real invertible n x n matrices so that B = (AT)-1. Show that Bm = (I - B1A1T)(AmT)+, where B1 = [b1, ..., bm], Bm = [bm+1, ..., bn], A1 = [a1, ..., am], Am = [am+1, ..., an]. Any pointers on how one would go about proving the above? I'm fresh out of ideas. I'm not sure if the above statement is even actually true. Using random matrices in matlab, I have not found any counterexamples, though.