Let A be an nxn matrix that is similar to an upper triangular matrix and has the distinct eigenvalues 1 , 2 ,

Let A be an nxn matrix that is similar to an upper triangular matrix and has the distinct eigenvalues λ₁, λ₂, ..., λ_k with corresponding multiplicities m₁, m₂, ..., m_k. Prove the following statements:

(a) tr(A) = ∑[i=1, k] m_iλ_i

(b) det(A) = (λ₁)m₁(λ₂)m₂... (λ_k)m_k