I am sorry if this comes accros as a low effort question, but i couldn't find any reliable source and i guess it's true but i would appreciate any confirmation.
Let $M$ be a orientable $m$-Manifold. Let $\alpha: M \to M$ be an involution, that is $\alpha(\alpha(x)) = x$. The standard examples of involutions i am aware of involve $\alpha_1(x) = -x$ and $\alpha_2(x) = \frac{1}{x}$. Which both qualify as orientation reversing functions.
I could imagine the given question to be true if every involution is a composition of either $a_1$ or $a_2$. However, i dont know whether this is true in general.
Highly appreciating any hint!
Additional question: Does the question i'm asking depend on whether the involution is fix point free?