Do u think is possible that a government lies to the world saying that a terrorist attack?

was on the name of Al-Qaeda when the Government really DID it to get economic benefits and affections from the town and immunity to attack Afganistan or Irak? There is a complicated question, but I was a survivor of an "islamic" attack and I have watched the doentary "9-11 Loose Change" in google and I am very confused.