Given

A =

1 0 -2

3 1 -6

0 1 1

I have worked out the inverse matrix and I have to use it to solve the system of equations

3x-y = 5

7x - 2y + 2z = 3

3x - y + z = 7

I can see that this is the inverse matrix, with rows 1 and 2 swapped (and -R1) but I don't know how this affects solving the equations. I have to use the inverse to solve. I really would like to understand what's happening here, rather tan just the answer. I'd appreciate any help.

Thanks