Calculating the Inverse of AB: A^(-1)=[4,0;-2,2], B^(-1)=[-2,0;-2,3]

[1question]

Homework Statement

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.)

Homework Equations

Inverse of AB = inverse of A*inverse of B

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.

 

[h.krish360]

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

 

[1question]

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

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).

 

[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).

 

[SteamKing]

In matrix calculations, AB does not equal BA. This is why matrix multiplication is called non-commutative. Your relevant equation no. 2 is false.

See: http://www.proofwiki.org/wiki/Inverse_of_Matrix_Product

 

[1question]

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).

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...