Science:Math Exam Resources/Courses/MATH220/December 2011/Question 01 (d)/Solution 1

Since the composition $\alpha \circ \beta$ is given by doing $\beta$ first and then $\alpha$, we must have that

$\begin{array}{r}1\mapsto 2\mapsto 3\\ 2\mapsto 1\mapsto 2\\ 3\mapsto 3\mapsto 4\\ 4\mapsto 4\mapsto 1\end{array}$

and so we have that $\alpha \circ \beta$ is given by

$\alpha \circ \beta =\left(\begin{array}{cccc}1& 2& 3& 4\\ 3& 2& 4& 1\end{array}\right)$