anonymous
  • anonymous
Hi does anyone know how to solve this problem??? Let A and B be square matrices of order 2 such that A-1 = 1 2 and (AB)−1= −2 3 -1 3 3 −4 find B..
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Here's a hint. A = [2 3;0 4] AB = [-1 4; 4 -3]
anonymous
  • anonymous
\[(AB)^-1 = (B)^-1 * (A)^-1\]
anonymous
  • anonymous
when you say A-1 you mean A^-1 (The inverse)?

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anonymous
  • anonymous
yes i mean the inverse @ daramda
anonymous
  • anonymous
Corec pointed you in the right direction, use that equation to set up another system of equations and solve for the inverse of matrix B. Then find the inverse of the inverse of matrix B which is the solution.
anonymous
  • anonymous
As long as I understand the question correctly (both A and B are square matrices): B=[(10/29), (-7/29); (25/29), (-3/29)}
anonymous
  • anonymous
10 7 5 3 THAT ARE THE VALUE OF B .
anonymous
  • anonymous
thank you all for your help! havent gotten around to doing it yet but will let you know if I get it. :-)
anonymous
  • anonymous
[10, 7; 5,3] is correct. I ran the math again on my solution, and it assigns [-2, 3; -7, -4] to (AB)^-1, so it looks like I failed at simple arithmetic. Nice catch corec ; )
anonymous
  • anonymous
Thanks

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