Matrix multiplication is not commutative.
How do you know if a matrix multiplication is commutative?
Matrix multiplication is always commutative if ...
- one matrix is the Identity matrix.
- one matrix is the Zero matrix.
- both matrices are 2×2 2 × 2 rotation matrices. ( basically case #2)
- both matrices are Diagonal matrices.
Is matrix multiplication always Abelian?
The sets Q+ and R+ of positive numbers and the sets Q∗, R∗, C∗ of nonzero numbers under multiplication are abelian groups. ... The set Mn(R) of all n × n real matrices with addition is an abelian group. However, Mn(R) with matrix multiplication is NOT a group (e.g. the zero matrix has no inverse).
