Consider the group of symmetries of a line and let $I$ be the trivial symmetry
- Is this group commutative?
- Is there a symmetry $a\neq I$ such that $a^3 = I$?
- If you combine a translation and a rotation do you get new kind of symmetry or another kind of rotation or translation?
- Is this group isomorphic to the group of symmetries of a circle?
This is very confusing, I know that I can use the number line as an example but how do I do that?