Exercise 1

Predict the result of each product with a permutation matrix and then check by multiplying it out.

• (a)  $\begin{pmatrix}0&1\\ 1&0\end{pmatrix}\begin{pmatrix}1&2\\ 3&4\end{pmatrix}$     (b)  $\begin{pmatrix}1&2\\ 3&4\end{pmatrix}\begin{pmatrix}0&1\\ 1&0\end{pmatrix}$     (c)  $\begin{pmatrix}1&0&0\\ 0&0&1\\ 0&1&0\end{pmatrix}\begin{pmatrix}1&2&3\\ 4&5&6\\ 7&8&9\end{pmatrix}$