# Homework Help: Find the inverse of AB:

1. Mar 9, 2013

### 1question

1. The problem statement, all variables and given/known data

Find the inverse of AB if A^(-1)= [4,0;-2,2] and B^(-1)=[-2,0;-2,3]. (See below for picture/additional information.)

2. Relevant equations

Inverse of AB = inverse of A*inverse of B

3. The attempt at a solution

Using above equation:

(AB)^(-1) = [4,0;-2,2]*[-2,0;-2,3] = [-8,0;0,6]

I don't understand why this is wrong. I calculated it by hand, and then used two different online matrix calculators when I was told it was wrong. The calculators agree with me. Am I entering it incorrectly? Here is a picture of the "full" question: http://imgur.com/foTsK2e.
Thanks.

Last edited: Mar 9, 2013
2. Mar 9, 2013

### h.krish360

Inverse of AB = inverse of B*inverse of A
Matrix multiplication does not commute!

3. Mar 9, 2013

### 1question

Um, what does commute mean in this context?

EDIT: Looked it up, and I don't understand why you say that. So what if BA doesn't work (haven't even tested it - don't see how it is applicable).

Last edited: Mar 9, 2013
4. Mar 9, 2013

### rcgldr

If you do the math to find A and B:

A = (A-1) -1

B = (B-1) -1

then multiply A and B, then take the inverse

(AB)-1

You'll find it's the same as (B-1) (A-1) and not the other way around. This is because matrix multiplicaion is associative, but not commutative (the next post has a link showing the math).

Last edited: Mar 9, 2013
5. Mar 9, 2013

### SteamKing

Staff Emeritus
6. Mar 10, 2013

### 1question

So the inverse of AB should be B^(-1)*A^(-1)? Tried it: got the question right.

Thank you.

EDIT: My textbook got it right, I just didn't pay attention. Whoops...

Last edited: Mar 10, 2013