Sums, Scalar Multiples, Composites and the Identity are Linear Operators

Let $K$ be a field, let $V$ be a vector space over $K$, let $S$ and $T$ be linear operators on $V$, and let $\lambda\in K$. Then each of the following maps from $V$ to $V$ is a linear operator on $V$.

1. (Sum) The map sending $u\in V$ to $S(u)+T(u)$.

2. (Scalar multiple) The map sending $u\in V$ to $\lambda\,S(u)$.

3. (Composite) The map sending $u\in V$ to $S(T(u))$.

4. (Identity) The map sending $u\in V$ to $u$.