Compute the set of fixed points of the following map:
$f(X) := (y,-x)$ when $X=(x,y)$
So for this, do I just have to solve the system of equation such as:
$x=y$
$-x=y$?
Plugging the first into the second gives -y=y, which only happens when y=0.
So then what would the set of fixed points be?
(1,-1)?