Answer
\[
MN=
\left[ {\begin{array}{cc}
IA+OC & IB+DO \\
EA+IC & EB+ID
\end{array} } \right]
\]
Work Step by Step
The product of \[
M=
\left[ {\begin{array}{cc}
I & 0 \\
E & I \\
\end{array} } \right]
\]
and
\[
N=
\left[ {\begin{array}{cc}
A & B \\
C & D \\
\end{array} } \right]
\] is
\[
MN=
\left[ {\begin{array}{cc}
IA+OC & IB+DO \\
EA+IC & EB+ID
\end{array} } \right]
\]