Isolate middle value from $3\times 3$ matrix Not trained in math the solution to this problem is not immediately apparent, plus I am working on a larger problem which I'd rather get to.
I'm trying to isolate the middle value from a $3\times 3$ matrix
Suppose my matrix is 
$$\begin{pmatrix}
\\ 5 & 7 & 3
\\ 4 & 13 & 9
\\ 9 & 9 & 1
\end{pmatrix}$$
I'd like to produce a matrix using linear algebra methods to get
$$\begin{pmatrix}
\\ 0 & 0 & 0
\\ 0 & 13 & 0
\\ 0 & 0 & 0
\end{pmatrix}$$
I do not want a simple answer like subtract
$$\begin{pmatrix}
\\ 5 & 7 & 3
\\ 4 & 0 & 9
\\ 9 & 9 & 1
\end{pmatrix}$$
Additionally, what is the terminology for this kind of derived matrix if there is one?
$$\begin{pmatrix}
\\ 0 & 0 & 0
\\ 0 & 13 & 0
\\ 0 & 0 & 0
\end{pmatrix}$$

$$\begin{pmatrix}0&0&0\\0&1&0\\0&0&0\end{pmatrix}\begin{pmatrix}5&7&3\\4&13&9\\9&9&1\end{pmatrix}\begin{pmatrix}0&0&0\\0&1&0\\0&0&0\end{pmatrix} = \begin{pmatrix}0&0&0\\0&13&0\\0&0&0\end{pmatrix} $$
The first matrix isolates the middle row and the last isolates the middle column.
Edit: These types of matrices are sometimes called $E_{ij}$, where $i$ is the row and $j$ is the column. So these would be $E_{22}$.
