You haven't given us F and you haven't given us what all the variables mean, but from what I got, I think you've done the following. You have created a generic matrix F with entries a,b,c,d,e and f. And then you have found the product FA and that's what you got on the bottom.
However, it's not 2 eqns 2 unknowns. It's 4 equations with 6 unknowns since you have a,b,c,d,e and f:
2a -b + 3c = 1
a -b + 2c = 0
2d -e + 3f = 0 and
d -e + 2f = 1