Let $V$ be a finite dimensional vector space over $F$ and $T$ be a linear operator defined on $V$. Then if $p(t)$ and $q(t)$ are polynomials defined over $F$, then the the operators $P(T)$ and $Q(T)$ commute.
Is the converse true? i.e
$AB=BA \implies \exists$ polynomials $p(t)$ and $q(t)$ over $F$ and a linear transformation $T$ such that: $p(T)=A$ and $q(T)=B$
A hint in the right direction would suffice.
