stion $33.$ Consider the following block matrices

$x=\left[\begin{array}{cc}\text{I}& A\\ B& \text{I}\end{array}\right],Y=\left[\begin{array}{c}C\\ D\end{array}\right],$

where $A$ is an $mn$ matrix and I denotes the identity matrices with appropriate sizes. Suppose that we can do the product $xY.$ How many rows do $C$ and $D$ have?

$($a$)$ There is no conclusion from the given information, we must know the size of $B.$

$($b$)$ Both $C$ and $D$ have $m$ rows.

$($c$)$ Both $C$ and $D$ have $n$ rows.

$($d$)C$ has $m$ rows and $D$ has $n$ rows.

$($e$)C$ has $n$ rows and $D$ has $m$ rows.