Let $\displaystyle m_{1},m_{2}$ be two $\displaystyle n\times n$ matrices, and consider the $\displaystyle 2n\times 2n$ block-matrix $\displaystyle M=\begin{pmatrix}m_{1} & -m_{2} \\ m_{2} & m_{1}\end{pmatrix}.$ Does there exist a formula for the determinant of $\displaystyle M$ in the general case wherenoassumptions on $\displaystyle m_{1}$ and $\displaystyle m_{2}$ 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.