Find (AB)^-1 with Given Matrices | Inverse of 2x2 Matrices

[Ownaginatious]

Homework Statement

Use the given matrices to find (AB)^-1

(These are 2 X 2 matrices, please ignore the fraction bar in between the top and bottom elements. I can't figure this stupid latex piece of crap out)

A$$^{-1}$$ = $$\left(\frac{\frac{1}{2}}{\frac{-1}{2}} \ldots \frac{\frac{-5}{2}}{\frac{3}{2}}\right)$$

B$$^{-1}$$ = $$\left(\frac{\frac{2}{3}}{\frac{-1}{3}} \ldots \frac{\frac{4}{3}}{\frac{5}{2}}\right)$$

Homework Equations

Only the one for inverse matrices which states,

(AB)$$^{-1}$$ = B$$^{-1}$$A$$^{-1}$$

The Attempt at a Solution

The answer I get in the end is:

(AB)$$^{-1}$$ = $$\left(\frac{\frac{-1}{3}}{\frac{-17}{12}} \ldots \frac{\frac{1}{3}}{\frac{55}{12}}\right)$$

But the book gets,

(AB)$$^{-1}$$ = $$\left(\frac{\frac{-1}{3}}{-1} \ldots \frac{\frac{1}{3}}{\frac{10}{3}}\right)$$

Am I the one doing something wrong, or is the book wrong?

Any help would be greatly appreciated.

Thanks!

 

[CompuChip]

If you copied the matrices correctly, your answer is correct.
If the 5/2 in (2,2)-entry of $B^{-1}$ is supposed to be 5/3 then the book is correct.

By the way, click the formula to see the LaTeX code:
$$A^{-1} = \begin{pmatrix} \frac{1}{2} & -\frac52 \\ \-\frac{1}{2} & \frac{3}{2} \end{pmatrix} = \frac12 \begin{pmatrix} 1 & -5 \\ -1 & 3 \end{pmatrix}$$

 

[Ownaginatious]

Nope, the book says what I wrote. I'm not surprised though; I've found several typos in the questions in this particular textbook...

Thanks a lot for the clarification, I thought maybe I was missing some obscure rule :p.

Also, thanks for showing how to use the LaTex code properly :)

 

[theallknower]

Homework Equations[/h2]

Only the one for inverse matrices which states,

(AB)$$^{-1}$$ = B$$^{-1}$$A$$^{-1}$$

I find it a lot more easy to calculate AB first,then the inverse...

just a tip,since the main question was already answered

 

[CompuChip]

I find it a lot more easy to calculate AB first,then the inverse...

just a tip,since the main question was already answered

In this case your approach would take longer, because you first have to calculate A and B from their inverses, then multiply them and finally take the inverse of that, while just multiplying the two given matrices in the correct order gives you the right answer immediately.