I puzzled over this one before getting it wrong. So, if the correct answer is "That is his mother's," is the Czech version literally "that is OF his mother"?
It is, literally.
Without specifying my/your/his in the same sentence you can use "matčino", "To je matčino", which would be literally "That is mother's".
Well, not sure. For me OF his mother suggests a little bit that it is made out of his mom. Let's not even go there....
Czech equivalent of that morbid though would be Je to z jeho matky.
Not sure what you were thinking about
I guess I'm trying to twist the Czech into something that makes sense (to me) in English. So now I'm carrying in my head "That is of mother of him," which, when untwisted, could be thought of simply as "That is his mother's." Now, if I can remember this, I'll be all set!