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Inverse of matrix AB?

  • #1

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[tex]^{-1}[/tex] = [tex]\left(\frac{\frac{1}{2}}{\frac{-1}{2}} \ldots \frac{\frac{-5}{2}}{\frac{3}{2}}\right)[/tex]

B[tex]^{-1}[/tex] = [tex]\left(\frac{\frac{2}{3}}{\frac{-1}{3}} \ldots \frac{\frac{4}{3}}{\frac{5}{2}}\right)[/tex]

Homework Equations



Only the one for inverse matrices which states,

(AB)[tex]^{-1}[/tex] = B[tex]^{-1}[/tex]A[tex]^{-1}[/tex]

The Attempt at a Solution



The answer I get in the end is:

(AB)[tex]^{-1}[/tex] = [tex]\left(\frac{\frac{-1}{3}}{\frac{-17}{12}} \ldots \frac{\frac{1}{3}}{\frac{55}{12}}\right)[/tex]

But the book gets,

(AB)[tex]^{-1}[/tex] = [tex]\left(\frac{\frac{-1}{3}}{-1} \ldots \frac{\frac{1}{3}}{\frac{10}{3}}\right)[/tex]

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

Any help would be greatly appreciated.

Thanks!
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
If you copied the matrices correctly, your answer is correct.
If the 5/2 in (2,2)-entry of [itex]B^{-1}[/itex] is supposed to be 5/3 then the book is correct.

By the way, click the formula to see the LaTeX code:
[tex]
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}
[/tex]
 
  • #3
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 :)
 
  • #4
Ownaginatious;2156299[h2 said:
Homework Equations[/h2]

Only the one for inverse matrices which states,

(AB)[tex]^{-1}[/tex] = B[tex]^{-1}[/tex]A[tex]^{-1}[/tex]
I find it a lot more easy to calculate AB first,then the inverse...

just a tip,since the main question was already answered
 
  • #5
CompuChip
Science Advisor
Homework Helper
4,302
47
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.
 

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