Problem #WSP-000298

Problem

There are six symmetries of an equilateral triangle: three reflections, and three rotations (thinking of the identity as one the rotations). Label the three reflections $s_1$, $s_2$ and $s_3$. Label the identity by $e$, rotation by ${120}^{\circ }$ as $r_1$, and rotation by ${240}^{\circ }$ clockwise as $r_2$.

Note the following definition: Each symmetry has an inverse. Suppose we apply symmetry $x$. Then there is some symmetry we can apply after $x$, which means that overall, we’ve applied the identity. What are the inverses of $r_1$ and $s_1$?