# Find $\det A$ and $Tr A$ if $\det(A+\sqrt[n]{3}I_n)=0$

$$A \in M_{n}(\mathbb{C})$$ and I have to find $$\det A$$ and $$Tr A$$ if $$\det(A+\sqrt[n]{3}I_n)=0$$. I observed that $$\sqrt[n]{3}$$ is an eigenvalue of $$A$$,but I don’t know how to continue.