Is my textbook wrong? My textbook says (without explaining how it is done): 
$$\begin{pmatrix} 
  1\ 2\ 3\ 4\\ 
  2\ 1\ 4\ 3 
\end{pmatrix}\begin{pmatrix} 
  1\ 2\ 3\ 4\\ 
  2\ 3\ 4\ 1 
\end{pmatrix}=\begin{pmatrix} 
  1\ 2\ 3\ 4\\ 
  3\ 2\ 1\ 4 
\end{pmatrix},$$
and as I understand this is obtained by doing calculations from left to right, but as I read here and elsewhere it should be done from right to left, like function composition...
So what i got is: 
 $\begin{pmatrix} 
  1\ 2\ 3\ 4\\ 
  2\ 1\ 4\ 3 
\end{pmatrix}\begin{pmatrix} 
  1\ 2\ 3\ 4\\ 
  2\ 3\ 4\ 1 
\end{pmatrix}=\begin{pmatrix} 
  1\ 2\ 3\ 4\\ 
  1\ 4\ 3\ 2 
\end{pmatrix}$,
or in cycle notation:
$(1,2)(3,4)(1,2,3,4)=(2,4)$ am I right?

Permutations are functions, so most people do the evaluation from right to left.
