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

${\begin{aligned}1\mapsto 2\mapsto 3\\2\mapsto 1\mapsto 2\\3\mapsto 3\mapsto 4\\4\mapsto 4\mapsto 1\end{aligned}}$

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

$\alpha \circ \beta ={\begin{pmatrix}1&2&3&4\\3&2&4&1\end{pmatrix}}$