10 Given the set $A=\left\{x \mid(a-1) x^{2}+3 x-2=0\right\}$, does there exist a real number $a$ such that the set $A$ has exactly two subsets? If it exists, find the value of the real number $a$ and the corresponding two subsets; if not, explain the reason.
(10) When $a=1$, the two subsets are $\varnothing,\left\{\frac{2}{3}\right\} ;$ when $a=-\frac{1}{8}$, the two subsets are $\varnothing,\left\{\frac{4}{3}\right\}$.