问题求解

听说这儿好多数学迷，数学牛人。

能不能请你们为我的朋友解答一道数学题？据说要求15分钟内就可以解答。

先谢谢了。

given permutation p = (3 4 1)(2 5) and q = (1 4 5 2), both in cycle notation and with permutation product from right to left, we can see that p q and q p result in a 3-cycle. Is this an accident ? If not, what are the properties causing it ?