# Relation between invariant Subspace and characteristic polynomial

Let V be a complext vector space of dimension=4:

$$f \in End(V)$$ with characteristic polynomial $$p_{f}(t)= (t − 1)^2. (t − 2)^2$$

Define $$X$$ as the set of W subspace of V such that dim W=2 and W is f-invariant. If $$|X|$$ is finite then $$|X|$$=3.

I tried to work it out using the 4 possible canonical Jordan form of $$f$$ and relating them to the minimal polynomial, yet I'm not sure about my work.