Commutation

You have seen commutation for both addition and multiplication of scalars:

• a+b=b+a
• a*b=b*a

Operation[a,b]=Operation[b,a]

The first time you didn’t have complications probably when you were working with matrices. More interesting still instead of

For some scenarios, the restrictions on the matrices make it such that AB = -BA. For these special situations, we say matrix multiplication is anticommutative. We run into this when we use matrices for work with quaternions.

If all matrices are diagonal, then AB=BA, the matrix multiplication is commutative.