How to calculate an All-Pass filter quantization coefficients Given 

$$H(z) = \frac{z^{-1}-0.8}{1-0.8z^{-1}}\text,$$

does the filter stay an All-Pass filter after quantization of coefficients?

If so, how can I prove it mathematically?
Hint:


Write the transfer with a general coefficient $a$ (instead of the value $0.8$) in the numerator as well as in the denominator.
Compute the magnitude of the numerator for $z=e^{j\omega}$.
Compute the magnitude of the denominator for $z=e^{j\omega}$.
Show that both magnitudes are equal, regardless of the value of the coefficient $a$, hence $H(e^{j\omega})=1$, i.e., the system is an allpass, even after coefficient quantization.