S.T the moment of a couple does not depend on the point about which the body rotates.

Explanation

Consider a couple as shown in Fig. 7.22 acting on a rigid body. The forces `F and -F` act respectively at points B and A. These points have position vectors `r_(1) and r_(2)` with respect to origin O. Let us take the moments of the forces about the origin.
The moment of the couple = sum of the moments of the two forces making the couple
`=r_(1)xx(-F)+r_(2)xxF`
`=r_(2)xxF-r_(1)xxF`
`=(r_(2)-r_(1))xxF`
But `r_(1)+AB=r_(2)`, and hence `AB=r_(2)-r_(1)`.
The moment of the couple, therefore, is `AB × F`.
Clearly this is independent of the origin, the point about which we took the moments of the forces.