This is one of the 117 mis-spellings listed as 'Common difficulties' in the section on 'Spelling' within 'Writing' in UEfAP.
Note that the noun library - which should be the centre of education, at least for students of the humanities - has two '-r-'s. The vowel between them is '-a-', even if it is pronounced (in RP) as the weak sound shwa, 'LIE -brer-y', IPA: /ˈlaɪb rər ɪ/, reduced by many speakers to 'lie-ber-y', /ˈlaɪb ər ɪ/. In American pronunciation, it is usually realized as 'LIE-brair-y', /ˈlaɪb ˌreɪr ɪ/. (Consequently, according to LPD, the word is less often mis-spelled or mis-pronounced by Americans.)
- Note that library/librairie is one of the false friends met in translation from the French. Librairie in French means 'bookshop': a place for selling and buying books, not (as in English library) a place for borrowing them, or a room for storing them.