To prove a ring is commutative, one must show that for any two elements of the ring their product does not depend on the order in which you multiply them. For example, if p and q are any two elements of your ring then p*q must equal q*p in order for the ring to be commutative.
Note that not every ring is commutative, in some rings p*q does not equal q*p for arbitrary q and p (for example, the ring of 2x2 matrices).
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It is no commutative.
That is true, matrix multiplication is not commutative.
Matrix addition is commutative if the elements in the matrices are themselves commutative.Matrix multiplication is not commutative.
Yes. Multiplication is commutative, just like addition.
The commutative property of addition can be stated as: a+b = b+a