Explain why matrix multiplication is not commutative.

[xsgx]

The title says it all.

Commutative* sorry
Mod note: fixed title.

 

[Mark44]

Why do you want to know?

 

[h6ss]

Let A = [a_ij] and B = [a_jk] where j ≠ k, then AB is defined, but BA is not.

But consider the case where i = j = k, so that A = [a_i] and B = [a_i] are square matrices.

Then, take for example i = 2 and calculate AB and BA. What do you find?

Generally, AB ≠ BA, for all values of i. It just stems from the definition of matrix multiplication.

 

[SteamKing]

Matrix multiplication is defined only for certain rectangular matrices A and B. The matrix product AB is defined only if the number of columns in A is equal to the number of rows in B. Assuming this condition is met, the product AB is defined, but the product BA may not be.

 

[Mark44]

h6ss and SteamKing,
Please hold off further comments until I can ascertain whether this is a homework question. If it is, it was posted in the wrong section with no efforts shown.