Does
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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.
We have
For non-commutative operators under some algebraic structure, it is not always true:
Let be the set of quaternions, and let .
Then
However, .
This is because .
In fact, .
Let be the symmetry group of elements, and let in cycle notation:
which are clearly unequal.