Explain why matrix multiplication is not commutative.

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The title says it all.

Commutative* sorry
Mod note: fixed title.
 
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Why do you want to know?
 
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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

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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.
 
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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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