Finding elements in $S_{3}$

Question

Question: In $S_{3}$, find elements $\alpha$ and $\beta$ such that $\left | \alpha \right |=2,\left | \beta \right |=2$ and $\left | \alpha \beta \right |=3$

I note that the permutation in $S_{3}$ is a product of transpositions.

Useful hints would be helpful

Thanks in advance

Answer 1

Take two different transpositions, for example $\alpha=(1\ 2)$ and $\beta=(1\ 3)$.