Character Analysis
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Mrs. Norris is a cat belonging to Hogwarts caretaker Argus Filch. She seems to act as a kind of spy for Filch, somehow informing him when students are breaking the rules or dirtying the castle. Mrs. Norris is the first victim of the Slytherin monster; she is found on Halloween night hanging by her tail from a torch bracket, stiff as a board. Filch thinks that Harry is the one who Petrified her because he knows that Filch is a Squib (a non-magical person with magic parents). Professor Dumbledore reassures him that this is not the case and Filch seems to feel better, but he still skulks "red-eyed through the corridors, lunging out at unsuspecting students and trying to put them in detention for things like 'breathing loudly' and 'looking happy'" (9.62).
By the way, J.K. Rowling has confirmed that the name "Mrs. Norris" comes from the horrible, interfering busybody Mrs. Norris in Jane Austen's Mansfield Park (source).