Matrix multiplication is associative, so the order of the multiplication doesn't matter mathematically. You might get small differences due to numerical effects. If you are getting something vastly different then maybe you can show us the exact code you are using and we can comment on it.
That being said, if A is 2x2 then the inverse of 
will only exist if A is full rank. And if that is the case then your equation reduces to alpha = [dx dy]*inv(A), in which case maybe you should be doing this instead: alpha = [dx dy]/A
will only exist if A is full rank. And if that is the case then your equation reduces to alpha = [dx dy]*inv(A), in which case maybe you should be doing this instead: alpha = [dx dy]/A Are you sure about the dimensions of A?
