linear algebra - Proof about diagonal matrices

Suppose that $A\in M_{n\times n}(\mathbb{R})$ such that their eigenvalues are $\{\lambda_1,\cdots, \lambda_n\}$, i.e. $\sigma(A)=\{\lambda_1,\cdots,\lambda_n\}$, then if the geometric multiplicity $mg_A(\lambda_i)$ is the same arithmetic multiplicity $ma_A(\lambda)$, we have that $A$ can be diagonal