SOLUTION —
Given determinant is satisfied, if $a=b=c$
$\begin{aligned}\Rightarrow \quad A=B=C & =60^{\circ} \\\therefore \sin ^2 A+\sin ^2 B+\sin ^2 C & =3 \sin ^2\left(60^{\circ}\right) \\& =3 \times\left(\frac{\sqrt{3}}{2}\right)^2=\frac{9}{4}\end{aligned}$
So, The correct option is (B).