If v is an eigenvector of A with corresponding eigenvalue λ, show that v is an eigenvectors of A^-1. What is its corresponding eigenvalue?
This should be rather easy. The notation, however, depends on whether you write vectors in rows or in columns.
If I use row vectors, then v being eigenvector means
.
What do you get if you multiply this equality by from the right?
(Obviously, you assume that A is invertible, even if you did not write this assumption explicitly.)