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\end{equation}  If we define an operation that is $RCR_{ij}(A):=R_{ij}$, remove column, row $ij$ on $A$, then this is expressible as  \begin{equation}  A^{-1}=\begin{bmatrix}   R_{11} & R_{12} R_{12}J  & R_{13} \\ R_{21} R_{21}J  & R_{22} & R_{23} R_{23}J  \\ R_{31} & R_{32} R_{32}J  & R_{33} \end{bmatrix} \end{equation}  Where \begin{equation}  J=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}  \end{equation}