This wiki is incomplete.
Is this true or false?
Why some people say it's true: It's easy:
Why some people say it's false: It's not that easy... there must be something I have missed...
The statement is .
The statement is true if the operator is commutative that is, and associative that is, This is always true with real numbers, but not always for imaginary numbers.
For non-commutative operators under some algebraic structure, it is not always true:
Let be the set of quaternions, and let .
This is because .
In fact, .
Let be the symmetry group of elements, and let in cycle notation:
which are clearly unequal.