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\end{equation}  This likely works because for any 2x2 matrix $|A|=-|AJ|=-|JA|=|JAJ|$.  Extrapolating backwards for a two by two matrix we get the correct formula on the proviso we definfe $J_1\equiv-1$. This makes some sense, as for any $J_nJ_n=I$ and $J_nJ_nA=A$.  We can further extrapolate to the inverse of a 1x1 matrix $A=A_{11}$, taking the $R_{11}$ element to be the zero matrix, the determinant of this matrix is $1$ and the reciprocal of the determinant of $A$ is then just the reciprocal of $A_{11}$, which again is the inverse of the 1x1 matrix.