Is digital up and down sampling linear/causal/time-invariant?
Upsampling and downsampling are both causal, since the output at time $m$ depends only on samples you've seen up time $m$. 

It is also linear (apply upsampling/downsampling to a x[n]+y[n] and see that you get a upsample/downsample x[n] + upsample/downsample y[n]). 

Downsampling not time invariant though - what happens if you downsample by 2 and consider inputting x[n] and x[n] delayed by 1 time unit? Now, what about upsampling?