Determine the inverse \(z\) transform of the following functions of the complex variable \(z\), supposing that the systems are stable:

(a) \(\frac{z}{z-0.8}\)

(b) \(\frac{z^{2}}{z^{2}-z+0.5}\)

(c) \(\frac{z^{2}+2 z+1}{z^{2}-z+0.5}\)

(d) \(\frac{z^{2}}{(z-a)(z-1)}\)

(e) \(\frac{1-z^{2}}{\left(2 z^{2}-1\right)(z-2)}\).