The expression aren’t I is often used in place of am I not, particularly in conversational speech.
Example 1 (incorrect usage): I’m going with you on vacation, aren’t I?
Although the use of this phrase is widespread, it is atrocious English that could be considered equivalent to you is, a phrase which most educated people abhor (although for some reason, these same people have no qualms about saying aren’t I). The correct form of the sentence in Example 1 is as follows:
Example 2 (correct usage): I’m going with you on vacation, am I not?
If you read this sentence aloud, it probably sounds awkward and formal, perhaps even a bit hoity-toity. However, it is correct English. If the phrase aren’t I is converted from a question to a statement, I aren’t, it becomes obvious that it is indeed grammatically incorrect.