I am working through some problems about modules in Dummit and Foote, and cannot figure this one out at all: 10.1.20
Let $\mathbb F = \mathbb R$ and let $V = \mathbb R^2$ and let $T$ be the linear transformation from $V$ to $V$ which is rotation clockwise about the origin by $\pi$ radians. Show that every subspace of $V$ is $\mathbb F[x]$-submodule for this $T$.
I just have no clue how to approach this question, and not sure how to prove this.
Any help would be appreciated, thank you!