SOLUTION: Please help me solve this problem (2x2 matrix) If A=[1 -2, 1 0] and AB=[1 0, -1 2]Find B. I tried multiplying A*AB changing the signs of AB but the answer did not come out

Algebra ->  Matrices-and-determiminant -> SOLUTION: Please help me solve this problem (2x2 matrix) If A=[1 -2, 1 0] and AB=[1 0, -1 2]Find B. I tried multiplying A*AB changing the signs of AB but the answer did not come out      Log On


   

Question 33642: Please help me solve this problem (2x2 matrix)
If A=[1 -2, 1 0] and AB=[1 0, -1 2]Find B.
I tried multiplying A*AB changing the signs of AB but the answer did not come out right.
Answer should be B=[-1 0, -1 1]
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
let us use variables:
B[a b, c d]
A=[1 -2, 1 0]
AB=[1 0, -1 2]
A[1 -2, 1 0]*B[a b, c d]
AB[a+b -2a, c+d -2c]=[1 0, -1 2]
from this, we know that a=0 and c=-1
AB[0+b 0, -1+d 2]=[1 0, -1 2]
from this, we know that b=1 and d=0
So..... B[0 1, -1 0]
I solved by using:
A[a b, c d]
is
................................
I a , b I
I c , d I