<s>[INST] Product of Permutations Can someone explain how to multiply two permutations? I cannot get myself to understand. Please be very simple and explain each step. 
 [/INST] If you have two permutations displayed in this form:
$$\sigma = \begin{pmatrix} 1 & 2 & 3 & 4 & 5 \\ 3 & 4 & 2 & 5 & 1\end{pmatrix}$$
and
$$\tau = \begin{pmatrix}1 & 2 & 3 & 4 & 5 \\ 5 & 4 & 3 & 2 & 1\end{pmatrix}$$
you can reorder the columns of $\tau$ so that the first line of $\tau$ matches the second line of $\sigma$, and you obtain $\tau = \begin{pmatrix}3 & 4 & 2 & 5 & 1\\ 3 & 2 & 4 & 1 & 5 \end{pmatrix}$, and $\tau\sigma$ now is described by the first line of $\sigma$ and the last line of $\tau$, i.e 
$$\tau\sigma = \begin{pmatrix}1 & 2 & 3 & 4 & 5\\3 & 2 & 4 & 1 & 5\end{pmatrix}$$
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