Let D be any division ring and p, q positive integers. The optimal version of Hua's fundamental theorem of geometry of square matrices has been known in all dimensions but the 2 x 2 case. We solve the remaining case by describing the general form of adjacency preserving maps phi : M-2(D) -> M-pxq(D). One of the main tools is a slight modification of known non-surjective versions of the fundamental theorem of affine geometry. (C) 2014 Elsevier Inc. All rights reserved.