Show the equivalence of these 4 statements

[mathtastic]

It is V a finite (non endless) K-vector space and f: V --> V.
Show that these statements are equivalent.

a) ker(f)=ker(f²)
b) im(f) ∩ ker(f) = {0}
c) V = im(f) ⊕ ker(f)
d) im(f) = im(f²)