I have two problems dealing with left eigenvectors:

(1) Show that a left eigenvectorycorrecpinding to the eigenvalue of A belonging to $\displaystyle M_n$ is a right eigenvector of A* corresponding to (with a bar over it).

(2) Show that ifyis a left eigenvector corresponding to the eigenvalue of A belonging to $\displaystyle M_n$ theny(with a bar over it)is a right eigenvector of $\displaystyle A^T$ corresponding to .

I know that the definition of left eigenvector states...the vectory≠ 0is said to be a left eigenvector of A if it satisfiesy*A =y*. Then is called a left eigenvector of A.