Three minor corrections should be sufficient to make this work for both, HTML and PDF output:
- remove the backslash before the closing bracket in
\right\) - delete the empty line in the middle
- specify the column alignment in each
arrayenvironment, e.g., with\begin{array}{cc}
–
$$
\left(\begin{array}{cc}
0.8944272 & 0.4472136\\
-0.4472136 & -0.8944272
\end{array}\right)
\left(\begin{array}{cc}
10 & 0\\
0 & 5
\end{array}\right)
$$