Two versions are given below; the information is exactly the same, just written slightly differently.
Version 1
Let \(\bS\) denote a matrix and \(\bT\) its inverse.
\[\bT = \left[ \begin{array}{cc} (\bS_{11} - \bS_{12} \bS_{22}^{-1} \bS_{21})^{-1} & -(\bS_{11} - \bS_{12} \bS_{22}^{-1} \bS_{21})^{-1}\bS_{12} \bS_{22}^{-1} \\\\ -\bS_{22}^{-1} \bS_{21} (\bS_{11} - \bS_{12} \bS_{22}^{-1} \bS_{21})^{-1} & \bS_{22}^{-1} + \bS_{22}^{-1} \bS_{21} (\bS_{11} - \bS_{12} \bS_{22}^{-1} \bS_{21})^{-1} \bS_{12} \bS_{22}^{-1}\end{array} \right]\]In particular, focusing on the upper left corner, note that
\[\bT_{11}^{-1} = \bS_{11} - \bS_{12} \bS_{22}^{-1} \bS_{21};\]this quantity is known as the Schur complement.
Version 2
Consider a matrix \(\M\) partitioned as follows:
\[\M = \left[ \begin{array}{cc} \A & \B \\\\ \B^T & \D\end{array} \right]\]Then
\[\M^{-1} = \left[ \begin{array}{cc} \A^{-1} + \F\E^{-1}\F^T & -\F\E^{-1} \\\\ -\E^{-1}\F^T & \E^{-1}\end{array} \right]\]where \(\E = \D - \B^T\A^{-1}\B\) and \(\F=\A^{-1}\B\). Here, \(\E\) is the Schur complement of \(\A\).