I am trying to show that a matrix A and A^t have the same eigenvalues. Well im sure its because det(a) = det(A^t), the characteristic polynomial is det(A-xI). But this question im trying to solve also asks for an example of a 2x2 matrix A where A and A^t have different eigenvectors. Im kinda lost of this one. Wouldn't they have the same eigenvectors because they have the same eigenvalues?