Hi! Can someone please explain:

In the following problem, let
A =

[1 2 −1 ]
[1 1 1]
[1 −1 0]
,

B =

[1 −1 0]
[1 1 1]
[1 2 −1]
.
Find an elementary matrix E that satisfies the given equation.
EA = B

Question

Hi! Can someone please explain: 


In the following problem, let
A = 

[1	2 −1	]
[1	1    1]
[1   −1    0] 
, 

B = 

[1 −1 0]	
[1   1  1]
[1   2 −1]
.
Find an elementary matrix E that satisfies the given equation.
EA = B

mathmale · Answer

I have a hunch that you could find E (which is probably a 3x3 matrix) by finding the inverse of matrix A and then multiplying EA = B by this inverse:$$EAA ^{-1}=BA ^{-1}$$

mathmale · Answer

This will leave you with matrix E on the left side and a 3 by 3 matrix on the right side.