Matrix help

[zzinfinity]

I need a little help with a homework question.

"Give an example to show that the product of two symmetric matrices is not necessarily symmetric. "

I've tried several symmetric matrices, and they all give a symmetric product. I can't think of another method other than just brut force trying a bunch of matrices. Any help will be very appreciated. Thanks!

 

[tkhunny]

Try the other brute force.

\(\displaystyle
\begin{pmatrix}
a & b \\
b & c
\end{pmatrix}
\cdot
\begin{pmatrix}
d & e \\
e & f
\end{pmatrix} =
\begin{pmatrix}
NotImportant & Important1 \\
Important2 & NotImportant
\end{pmatrix}\)

With a little effort, find \(\displaystyle Important1 \ne Important2\)