Proof about diagonalizable Matrix

Question

The proof said the following, let $A \in M_{n \times n}(\mathbb{C})$ such that $A^r=I_{n \times n}$ for some $r \in \mathbb{N},r>0$ then $A$ is diagonalizable. Mi attempt is the next, since $A$ is equal to the identity matrix, then we can approach the jordan normal form of the $A$, but, i can´t see, the zise of the jordan blocks. someone who give me a hint, or in her case the proof