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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.

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