My question could be considered more general than the $5 \times 5$ case, but I'm wondering how when using Blockwise inversion you can select an appropriate $\bf A$, $\bf C$, and $\bf B$ such that the matrix sizes confirm for multiplication of $\textbf{D} - \textbf{C}\textbf{A}^{-1}\textbf{B}$
For example,
- $\bf A$ is $2 \times 2$
- $\bf B$ is $2 \times 3$
- $\bf C$ is $3 \times 2$
- $\bf D$ is $3 \times 3$
Lead to $\textbf{A}^{-1}\textbf{B}$ being a $2 \times 3$ matrix which is improper for multiplication by a $3 \times 3$.
Trying $\bf A$ being $3 \times 3$ seemed to lead to the same issue, am I missing something?