Let $V$ be a vector space over $\mathbb{R}$ with dimension $n \geq 2$. Suppose $A$ $\in L(V, V)$ is a nonzero transformations such that for each subspace $W$ of $V$ such that $AW \subset W$ we have $W = 0$ or $W = V$.
Question: What should it tell me about A when the only invariant subspaces under A are trivial? Is there a useful theorem I'm not familiar with that I could look up to understand this better?