Answer
$\left[\begin{array}{cc}
\mathrm{W} & \mathrm{X}\\
-\mathrm{E}\mathrm{W}+\mathrm{Y} & -\mathrm{E}\mathrm{X}+\mathrm{Z}
\end{array}\right]$
Work Step by Step
Partitioned matrices can be multiplied by the usual row-column rule as if the block entries were scalars, provided that for a product $AB$, the column partition of $A$ matches the row partition of $B$.
$\left[\begin{array}{rr}
\mathrm{I} & 0\\
-\mathrm{E} & \mathrm{I}
\end{array}\right]\left[\begin{array}{ll}
\mathrm{W} & \mathrm{X}\\
\mathrm{Y} & \mathrm{Z}
\end{array}\right]=\left[\begin{array}{rr}
\mathrm{I}\mathrm{W}+0\mathrm{Y} & \mathrm{I}\mathrm{X}+0\mathrm{Z}\\
-\mathrm{E}\mathrm{W}+\mathrm{I}\mathrm{Y} & -\mathrm{E}\mathrm{X}+\mathrm{I}\mathrm{Z}
\end{array}\right]$
$=\left[\begin{array}{rr}
\mathrm{W} & \mathrm{X}\\
-\mathrm{E}\mathrm{W}+\mathrm{Y} & -\mathrm{E}\mathrm{X}+\mathrm{Z}
\end{array}\right]$
