# Homework Help: Basic matrix multiplication

1. Feb 19, 2014

### PsychonautQQ

1. The problem statement, all variables and given/known data
This isn't homework, but I didn't know where else to ask and I have a test in an hour and a half. The study guide says be able to explain why statements like (A+B)^2 = A^2 + 2AB + B^2 are bogus when dealing with matrix's. Is it because (A+B) = (B+A) but (A+B)^2 /= (B+A)^2 or something? Thx in advance

2. Relevant equations

3. The attempt at a solution

2. Feb 19, 2014

### tiny-tim

Hi PsychonautQQ!

In any algebra, you can use the distributive law.

So (A + B)(A + B) = AA + BB + AB + BA.

Sooo … ?

3. Feb 19, 2014

### PsychonautQQ

well in matrix multiplaction, AB /= BA.. so in that regard it differs from normal algebra. My study guide says "Be able to explain why statements like (A+B)^2 = A^2 + 2AB + B^2 are nonsense.. and you are saying it's not nonsense?
conflicted ;-/

4. Feb 19, 2014

### HallsofIvy

The crucial point is that matrix multiplication is NOT commutative. That is, in general, AB is NOT equal to BA so in tiny-tim's calculation, (A+ B)(A+ B)= AA+ BB+ AB+ BA is NOT equal to $$A^2+ B^2+ AB+ AB= A^2+ B^2+ 2AB$$.