Prove that the eigenspace of $\displaystyle T$ corresponding to $\displaystyle \lambda$ is the same eigenspace of $\displaystyle T^{-1}$ corresponding to $\displaystyle \lambda^{-1}$.

I just want to know how do you show an eigenspace of $\displaystyle T$ corresponding to $\displaystyle \lambda$ ?

would it just be $\displaystyle E_{\lambda} = \{ X \in V: T(x) = \lambda (x) \} = N(T-\lambda I_V) $ ?