Let R be a ring with unity and let End((R, +)) be the ring of endomorphisms of (R, +). Let a ∈ R, and let λ_a : R → R be given by λ_a(x) = ax for x ∈ R. 

a. Show that λ_a is an endomorphism of (R, +). 

b. Show that R' = {λ_a | a ∈ R} is a subring of End ((R, +)). 

c. Prove the analogue of Cayley's theorem for R by showing that R' of (b) is isomorphic to R.