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It looks like you want to treat the first equation as polynomial, meaning the equality of the coefficients for each monomial in theta's. If so, you need to add those equalities as individual equations:
R.<theta_0,theta_1> = SR[]
aVars=var(['a_00', 'a_01', 'a_10', 'a_11'])
eqL=[]
eqL.extend( ( 3*theta_0^2 + 9*theta_0*theta_1 + 5*theta_1^2 - \
(a_00*theta_0^2 + a_01*theta_0*theta_1 + a_10*theta_0*theta_1 + a_11*theta_1^2) ).coefficients() )
eqL.append(-a_01*a_10 + a_00*a_11 == 1)
show( solve(eqL,aVars) )
which gives exactly the two solutions you want.
