Does Newton's generalized binomial theorem work on a matrix?

Question

My question is that does Newton's generalized binomial theorem work on a matrix? In other words, for a Hermitian matrix $X$ and a real number $r$, is the following statement correct? Is there any condition on $X$ that makes the series valid/invalid? $$(I+X)^r=\sum_{k=0}^{\infty} \binom{r}{k} X^k$$