I know that composition of a rotation and reflexion of a regular $n-$gon in plane is reflexion and can be proved by using rotation and reflexion matrices . But I want to prove it by the fixed point method i.e. as non-trivial rotation has one fixed point that is center of $n$-gon, whereas reflexion has infinite many fixed points which are points of the line of reflexion. Now I am unable to prove that composition of reflexion $S$ and rotation $R$ has infinite many fixed points to become reflexion. Please suggest . Thank you .
2026-03-29 04:44:02.1774759442
Composition of rotation and reflexion of two symmetries of a regular $n$-gon.
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