Polynomial ring/Substitution/Matrix product/Exercise

Let

$f,g\colon V\longrightarrow V$

be endomorphisms on a ${}K$-vector space ${}V$, and let ${}P\in K[X]$ be a polynomial. Show that the equality

${}P(f\circ g)=P(f)\circ P(g)\,$

does not hold in general.

Create a solution