First, let x, y be the right and left eigenvectors
let λ1 and λ2 be different eigenvalues
So, I can consider Ax=λ1x and then I will find the result and (λ2-λ1)y*x=0
Since λ2 is not equal to λ1, y*x=0 => Orthogonal
However, how to prove two eigenvectors corresponding to the same eigenvalue of a matrix cannot be orthogonal to each other?