Let be two matrices, and consider the block-matrix Does there exist a formula for the determinant of in the general case wherenoassumptions on and are being made? The formulas for the determinants of block matrices given in Determinant - Wikipedia, the free encyclopedia or http://www.mth.kcl.ac.uk/~jrs/gazette/blocks.pdf, Eqs. (13)-(16) for the latter, are of no use, as they make assumptions of either invertibility or commutativity.