Please study this equation extensively while continuing in multiplying it by itself.

R_μν - 1/2 g_μν R + Λg_μν = κT_μν 

(R_μν - 1/2 g_μν R + Λg_μν) * (R_μν - 1/2 g_μν R + Λg_μν) = 

R_μν * R_μν - 1/2 g_μν * R_μν * R_μν + Λg_μν * R_μν - 1/2 g_μν * R_μν * g_μν R + Λg_μν * R_μν * g_μν

R_μν * R_μν - 1/2 g_μν * R_μν * R_μν + Λg_μν * R_μν - 1/2 g_μν * R_μν * g_μν R + Λg_μν * R_μν * g_μν =

κT_μν * R_μν - 1/2 κT_μν * g_μν * R_μν + κT_μν * Λg_μν - 1/2 κT_μν * R_μν * g_μν + κT_μν * Λg_μν * g_μν

κT_μν * R_μν - 1/2 (κT_μν * g_μν + κT_μν * Λg_μν) + 1/2 (κT_μν * g_μν * R + κT_μν * Λg_μν * g_μν) =

κT_μν * R_μν - 1/2 κT_μν * g_μν (1 + Λ) + 1/2 κT_μν * g_μν R 

κT_μν * (R_μν - 1/2 g_μν (1 + Λ)) + 1/2 κT_μν * g_μν R = 

κT_μν * (R_μν - 1/2 g_μν (1 + Λ)) * (1 + 1/2 g_μν) 

κT_μν * (R_μν - 1/2 g_μν (1 + Λ)) * (3/2) = 

1.5 * κT_μν * (R_μν - 1/2 g_μν (1 + Λ)) 

1.5 * κT_μν * (R_μν - 1/2 g_μν (1 + Λ))