Rotation Rules

Let 𝒯𝐝 denote the translation operator (displacement vector 𝐝 ); let 𝒟(𝐧̂, ϕ) denote the rotation operator (n? and ϕare the axis and angle of rotation, respectively); and let πdenote the parity operator. Which, if any, of the following pairs commute? Why? (a) ℐd and 𝒯𝐝^' (d and 𝐝^' in different directions). (b) 𝒟(𝐧̂, ϕ) and 𝒟(𝐧̂^', ϕ^')(𝐧̂ and 𝐧̂^' in different directions). (c) ℐd and π(d) 𝒟(𝐧̂, ϕ) and π | Numerade