Show that $\tau_1\tau_2$ of order $2$ or $3$, given that $\tau_1$ and $\tau_2$ are distinct transpositions.
I know that every cycle can be factored as a product of transpositions. But I'm not sure how to prove the order of $2$ or $3$.
Show that $\tau_1\tau_2$ of order $2$ or $3$, given that $\tau_1$ and $\tau_2$ are distinct transpositions.
I know that every cycle can be factored as a product of transpositions. But I'm not sure how to prove the order of $2$ or $3$.