Let T d denote the translation operator (displacement vector d); D (n, ), the rotation operator (n

Let T_d denote the translation operator (displacement vector d); D(n, Φ), the rotation operator (n and Φ are the axis and angle of rotation, respectively); and r the parity operator. Which, if any, of the following pairs commute? Why?

a. T_d and T_d (d and d’ in different directions).

b. D(ñ, Φ) and D(ñ, Φ) (ñ and n’ in different directions). 

c. T_d and π.

d. D(n, Φ) and π.