So $Ax=\lambda x$ where $A$ is the matrix, $\lambda$ and $x$ its eigenvalue and eigenvector resptectively.
Now I have another matrix similar to $A$ i.e. $B=TAT^{-1}$
I'll let a vector $y$ which is an eigenvector of $B$, i.e. $By=\mu y$ where $\mu$ is its ($B$'s) eigenvalue.
I have to now prove that $By=\mu x$.
Some maths leads me to
$By = TAT^{-1}y$ but here I'm stuck. This answers wants me to assume $y=Tx$ which will essentially solve it but why/how is $y=Tx$?