the eigenvectors of two different square matrices that have the same eigenvalue

I have two square matrices $Y$ and $Z$ size $n$, and matrix $M = Z^{-1}YZ$ eigenvalue is the same as Matrix $Y$'s eigenvalue. I have been able to prove that the eigenvalues are the same, and thus the characteristic polynomial of $Z^{-1}YZ$ $=$ $Y$ as the $|Y| = |Z^{-1}YZ|$ because the determinants are commutative and the determinant of an inverse matrix is $1/|Matrix|$. However, the eigenvectors will be different, am stuck here.

To put it more clearly:

What are the eigenvectors of matrices $Y$ and $Z^{-1}YZ$, they are both square matrices $n$ and the eigenvalues of $Y$ are the same as $Z^{-1}YZ$?