Downsampling and Then Upsampling
You will get 

$Y(z) = \frac1M\sum_{m=0}^{M-1} X(e^\frac{-j2\pi{m}}M*z)$



If you were to upsample first and then downsample you would get

$Y(z) = \frac1M\sum_{m=0}^{M-1} X(e^{-j2\pi{m}}*z)$

which just simplifies to (since $e^{-j2\pi{m}}=1$ for $m\in\mathbb{Z}$)

$\frac1M\sum_{m=0}^{M-1} X(e^{-j2\pi{m}}*z) = \frac1M\sum_{m=0}^{M-1} X(z) = X(z)$

Basically, if you upsample and downsample you can perfectly reconstruct the signal but if you downsample and then upsample, you are aliasing in the summation over rotations in the z-domain of the input.