Answer
$I_{m}-(-C)\left(A-B C-s I_{n}\right)^{-1} B$
Work Step by Step
From Exercise $15,$ we know that the Schur complement of $A_{11}$ in the block matrix
\[
\left[\begin{array}{ll}
A_{11} & A_{12} \\
A_{21} & A_{22}
\end{array}\right]
\]
is $A_{22}-A_{21} A_{11}-1_{A_{12}}$. So let's get that for the matrix
\[
\left[\begin{array}{cc}
A-B C-s I_{n} & B \\
-C & I_{m}
\end{array}\right]
\]
(Schur complement of $\left.A-B C-s I_{n}\right)=I_{m}-(-C)\left(A-B C-s I_{n}\right)^{-1} B$
\[
=\square_{m}+C\left(A-B C-s I_{n}\right)^{-1} B
\]
