Explain why matrix multiplication is not commutative.

xsgx

The title says it all.

Commutative* sorry
Mod note: fixed title.

Last edited by a moderator:

Mark44

Mentor
Why do you want to know?

h6ss

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

But consider the case where i = j = k, so that A = [ai] and B = [ai] 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

Staff Emeritus
Homework Helper
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

Mentor
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.

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