Problem 9. Let R, = (A - I)¹ and R, = (A - µl)-1 be the resolvents corresponding to the points A and μ. Prove that RR = RμR₂ and - - R₁ — R₂ = (µ — λ)RR₂. Hint. Multiply both sides of (19) by (A - N)(A — µI). (19) Comment. It follows from (19) that if A, is a regular point of A, then the derivative of R, with respect to A at the point λ0, i.e., the limit - lim Rio+Aλ Δλ AX-0 R (in the sense of convergence with respect to the operator norm) exists and equals R₁₂.