Symmetry Group of Line Segment/Cayley Table

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Cayley Table of Symmetry Group of Line Segment

The Cayley table of the symmetry group of the line segment can be written:

 & e & r \\

\hline e & e & r \\ r & r & e \\ \end{array}$


$e$ is the identity mapping
$r$ is the plane rotation of $180^\circ$ about the midpoint of $AB$.