linear algebra - Eigenvalues of diagonal matrix

Problem:

Let $A$ ∈ $\Bbb C^{n×n}$ and let $A$ be a diagonal Matrix with entries $\lambda_1, \ldots, \lambda_n$ ∈ $\mathbb{C}$ Determine spec($A$*$A$)

I think it is clear that the spec ($A$ *$A$) = {$\lambda_1, \ldots, \lambda_n$}, as the eigenvalues of a diagonal matix are just the elements on the diagonal. Could someone appove my thoughts?