Задача 13.

1) Show that for any $a,b\in S_n$ there are unique $x,y\in S_n$ such that $ax=b,\,ya=b$. Is it always true that $x=y$? 2) Show that for any $a,b,c\in S_n \\ (a=b)\Longleftrightarrow (ac=bc)\Longleftrightarrow (ca=cb)$.