0
$\begingroup$

This question already has an answer here:

Let $\bar m$ be the isometry sending a point $P$ to its opposite point $-P$, show that $\bar m$ commutes with any isometry of $S^2$

I know I can use the fact that isometries preserve distances, but do I need to individually apply this to each type of isometry?

$\endgroup$

marked as duplicate by user99914, Namaste, Shailesh, Did, JonMark Perry Mar 7 '18 at 9:22

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

0
$\begingroup$

What you want to prove is that, for each $P\in S^2$, $-f(P)=f(-P)$. Bu this is what was proved here.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.