Can a diffeomorphism not be an immersion or a submersion

Question

This may be a stupid question, but I have not seen anywhere that it is said that a diffeomorphism must be an immersion and a submersion. Therefore I am asking the following two questions:

(I) Is a diffeomorphism between smooth manifolds necessarily a submersion?

(II) Is a diffeomorphism between smooth manifolds necessarily an immersion?

(III) If either (I) or (II) aren't true, can someone help by giving a counter example?

Thanks in advance.

Answer 1

Since the derivative of a diffeomorphism at every point is bijective, every diffeomorphism is both a submersion and an immersion.