Let A = (aij) ∈ M atK (n). A Tracef Definition is Tr(A) = a11 + a22 + · · · + ann (cross number of ads). a) Prove that PA(λ) = det(A − λI) = (−1) n (λ) n- Tr(A) n − 1 + · · · + (- 1) n det A). b) Prove det (P −1AP - λI) = PA(λ), for every P match. c) Prove Tr(A) = Tr(P −1AP), with every inverse matrix P. d) Suppose 1, · · ·, n K, are eigenvalues ​​of A. Calculate Tr(A) and det A through that private value