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Tranquility
2005-Mar-03, 02:33 PM
I dont understand the concept of why an arithmetic rule like (a+b)^2 = a^2 + 2ab + b^2 and (a+b)(a-b) = a^2 - b^2 doesn't work when a and b are replaced by square matrices. I can prove it by actually doing it, but what is the actual explanation for this? Is it only because matrix multiplication is not commutative or are there other reasons for why these arithmetic rules don't work for matrices?

A Thousand Pardons
2005-Mar-03, 03:04 PM
Yes. For instance, in one of the steps of the algebra, you have ab+ba. In the matrices, this will only be equal to 2ab if ba equals ab--which is the commutative property.

Tranquility
2005-Mar-03, 04:22 PM
Oh alright. Thanks! I didn't really understand what "it's not commutative" meant in the first place. Thanks a lot.