9. Let the function $f(x)=\frac{a x}{2 x+3}$, if $f[f(x)]=x$ always holds, then the value of the real number $a$ is
$$
f[f(x)]=\frac{a \cdot \frac{a x}{2 x+3}}{2 \cdot \frac{a x}{2 x+3}+3}=\frac{a^{2} x}{2 a x+6 x+9}=x \Rightarrow(2 a+6) x+9=a^{2} \Rightarrow a=-3 .
$$