Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have a problem that I would like to check:

Expand $(A+B)^3$ where $A$ and $B$ are matrices.

Is this right? $$ A^3+A^2B+ABA+AB^2+BA^2+BAB+B^2A+B^3 $$ Thanks.

share|cite|improve this question

Yes, you've got it.

It is probably easiest to start off with $$ (A+B)^2=A(A+B)+B(A+B)=A^2+AB+BA+B^2. $$ From here, we find $$ (A+B)^3=(A+B)(A^2+AB+BA+B^2)=A^3+A^2B+ABA+AB^2+BA^2+BAB+B^2A+B^3, $$ as you claimed.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.