(a) Show that the sample variance is unchanged if a constantcis added to or subtracted from each value in the sample.

(b)Show that the sample variance becomes $\displaystyle c^2$ times its original value if each observation in the sample is multiplied by c.

This was something our professor gave us to do. I showed both by using problem examples from our textbook, but he said that it would be wise to be able to give a general proof for each, should it come up on our exam. I've never really done any proofs so I'm at a bit of a loss as where to start and whatnot. I'll be trying to figure this out but any help would definitely be appreciated.