Question

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..

Answer 1

Here's a hint. A = [2 3;0 4] AB = [-1 4; 4 -3]

Answer 2

\[(AB)^-1 = (B)^-1 * (A)^-1\]

Answer 3

when you say A-1 you mean A^-1 (The inverse)?

Answer 4

yes i mean the inverse @ daramda

Answer 5

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.

Answer 6

As long as I understand the question correctly (both A and B are square matrices):

B=[(10/29), (-7/29); (25/29), (-3/29)}

Answer 7

10 7
5 3
THAT ARE THE VALUE OF B .

Answer 8

thank you all for your help! havent gotten around to doing it yet but will let you know if I get it. :-)

Answer 9

[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 ; )

Answer 10

Thanks