I wonder if this doesn't make sense.If it is an unspecific library, you can use "a library" and for a specific library, "the library". My acquaintance answered with this, but got no mark for this part in a midterm of a Korean middle school. I need your clear answer.
ex)I wonder whether I can borrow the book at a library.
It's entirely understandable. Personally, I would say "from the library", but you are "at a library" at the point where you take the book to the desk and actually go through the borrowing procedure.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.
Nor do I. I think the tester ruled it out because people tend to have a local library that they refer to as 'the library'. For example, if I say to MrsK 'I'm going to the library' she knows that I mean Spencers Wood library. If I mean some other library - say Reading University library - then I specify that.
But the question 'I wonder whether I can borrow the book at a library' means 'I wonder whether there's a library somewhere where I can borrow the book' - perhaps for some reason the speaker thinks it's not the sort of book a library would stock.