Can I prove there are more than 1 fixed points of an affine map?

Question

If I have a map of the form $Mr+c $ where $M$ is a real matrix, $r$ is a point, and $c$ is a constant vector, how could I show that this transformation has more than 1 fixed point for a specific case where is does? I looked into the Lefschetz fixed point theorem but couldn't tell if I can use that or how.