For the first matrix, maybe a simpler example is M = [1 1; 0 0]. Then [1; 0] is a right eigenvector with eigenvalue 1, but [1 0] M = [1 1].
For the first matrix, maybe a simpler example is M = [1 1; 0 0]. Then [1; 0] is a right eigenvector with eigenvalue 1, but [1 0] M = [1 1].