Задача 7.

Show that the following are true: 1) For any permutation $a\in S_n$ we have $ae=ea=a$. 2) For any permutations $a,b,c\in S_n$ we have $(ab)c=a(bc)$. 3) For any permutation $a\in S_n$ there is a unique permutatioin $b\in S_n$ such that $ab=ba=e$.