# Thread: A little linear algebra help

1. Established Member
Join Date
Mar 2004
Posts
1,163

## A little linear algebra help

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?  Reply With Quote

2. 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.  Reply With Quote

3. Established Member
Join Date
Mar 2004
Posts
1,163
Oh alright. Thanks! I didn't really understand what "it's not commutative" meant in the first place. Thanks a lot.  Reply With Quote

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•