there exists vector space $V$ and linear operator $T$ such that $V$ has exactly three invariant subspaces under T?

Question

First of all, i thought there exists searching for some case with an example, but i don't find. Someone has seen the solution of this problem before? Sorry about my english...

Answer 1

Hint 1

Take $V$ to be $2$-dimensional.

Hint 2

What happens if $T$ has two distinct eigenvalues in the underlying field?

Hint 3

Can you build an example with $T$ having one eigenvalue with multiplicity two in the underlying field?