While the Matrix Trilogy may seem to be a deep and thoughtful movie, similar to Christianity, in fact it has a lot of anti-biblical teaching. See The Matrix and Presuppositional Apologetics for a detailed discussion of this, with quotes from the movie.
provide pdf discussion materials regarding Worldview and the Matrix Trilogy.
Note: by linking to these studies, I am in no way suggesting I agree 100% with everything in their Bible studies or on their websites. I am giving these links as a suggestion, for further information, for use in personal or homeschool situations. I expect that you will be measuring each question, each study, and each website with the same wariness as you measure any new information.