is the sentence "j'ai allé a le cinema" correcte ?

No it is not; There are two mistakes, can you find at least one of them?          * ... * First, in French you can't say "j'ai allé": you say "je suis allé"; you always use the auxiliaire 'etre' before the verb aller in the perfect tenses.  Second, you can't say "a le cinéma"; you have to say "au cinéma". in fact, when the subject (cinéma in this case) is masculine, you have to use au (je vais au supermarché, au tennis...); when it is feminine, you say "à" (je vais à l'epicerie, à la plage...); note: I would further develop my answer if I think it is appropriate; Thus I would/could add the following: when you are going to some shops, there's a trick: for example, in French, to say "I'm going to the barbers", we say "Je vais chez le coiffeur": because we don't talk about the place, but about the job of the people working there, we say 'chez'. e.g. chez le boucher, chez le boulanger, etc...