I am trying to prove that similar nxn matrices A and B share the same eigenvalues and characteristic polynomial.
I am not sure how to start, but I am tempted to start with something like
$$tr(A) = tr(B)$$
$$det(A) = det(B)$$
since we know that the matrices are similar.
But, this approach sort of seems to be using what I am trying to prove.
Is this a valid approach? Or, should I head in another direction instead?