Clear[a,b,q,G,IG, s]
F=12
a=0.4082
b=2*a

q={0,-2F,0,F}
G={{-1,-b,0,b},{0,a,0,a},{0,0,-1,-b},{0,0,0,-a}}
MatrixForm[%]
IG=Inverse[G]
MatrixForm[%]
s=-IG.q