I'm trying to prove that the subset of linear transformations given below is a group:
Let $T^n$ denote the n-fold composition of any $T∈ℒ(V)$. For instance, the two fold composition $T\circ T$ is denoted $T^2$.
Let $T∈ℒ(V)$ such that $T≠I$ and $T^n=I$. Show that $C_n=\{I^{},T^{},T^2,...T^{n−1}\}$ is a group.