Question

let A be an nxn matrix that is similar to an upper triangular matrix and has the distinct eigenvalues lambda_1, lambda_2,..., lambda_k with corresponding multiplicities m_1,m_2,...,m_k. Prove the following.

a. tr(A) = Sum(m_i*lambda_i)

b. det(A) = (lambda_1)^m_1 * ... * (lambda_k)^m_k