Solution
= Solution
\b[No.] In $S_3$, take $x=(12)$ and $y=(123)$. Their orders are two and three, but $xy$ is a transposition and has order two.
= Solution
\b[No.] In $S_3$, take $x=(12)$ and $y=(123)$. Their orders are two and three, but $xy$ is a transposition and has order two.