The commutator is stationary.

• A. True
• B. False
• C. Not specified
• D. Sometimes

Answer: (B)

The concept being tested is whether a commutator can be assumed to be constant over time or configuration. A commutator AB − BA measures how much two operations fail to commute. If both operands are fixed, time-invariant operators, then AB − BA is a fixed quantity and would be stationary. However, in robotics and dynamic systems, those operators often depend on the state or time (for example, on joint angles or configuration). As the system moves, the product AB and the reversed product BA can change, so the commutator itself becomes a function of the state and is not guaranteed to be stationary. Hence, saying the commutator is stationary is not generally true; it only stays stationary in the special case where both operands are constant.