Let $T:V \longrightarrow V$ a linear operator, where $V$ is a vector space over the field $\mathbb{K}$. Show that if $p(x),q(x)\in \mathcal{P}(\mathbb{K})$, then
$(p\cdot q)(T)(v)=p(q(T))(v), \ \ \forall v\in V.$
I have some examples but I get no such equality. I am taking $p \cdot q $ as the product of polynomials, as in the book i'm following do not indicate the meaning of that product. Could anyone help me or give me some pointers?