Let $G$ be a group and $\rho: G \to GL(V)$ a representation. Show that if $W$ is a $G$-invariant subspace of $V$, then $\rho(G)W \subseteq W$.
Let us systematically break down the solution strategies for each major section. Dummit And Foote Solutions Chapter 14
For students who want to learn more about Galois Theory and Abstract Algebra, we recommend the following resources: Let $G$ be a group and $\rho: G \to GL(V)$ a representation