The minimal polynomial of $A$ divides $x^{2013} -1$. Prove that $A$ is diagonalizable over the complex field.

Question

$A$ is a $n\times n$ real matrix. The minimal polynomial of A divides $x^{2013} -1$.

I need to prove that:

(1) A is diagonalizable over the complex field.

(2) If A is diagonalizable over the reals, then it must be the identity matrix.

At first I want to show that the minimal polynomial is consisted of different linear factors. I know that over the complex field every polynomial is decomposed to linear factors, but how can I prove that they are different?