Let $A$ be a closed densely defined operator on some Hilbert space $H$ with non-empty resolvent set $$ \rho(A)=\{ \lambda \in \mathbb{C} ; (\lambda - A)^{-1} \in L(H) \}. $$ Then the operators $A^n$ are closed and densely defined for all integers $n \geq 0$.
Question: I was able to show that $A^n$ is closed but why is it also densely defined?