The correct answer is: A. me
The sentence “He is richer than I am” is in the comparative form. In the comparative form, we use the word “than” to compare two things. The subject of the sentence is “he”, and the object of the sentence is “I”. The verb is “is”. The adjective is “richer”.
The correct pronoun to use after “than” is the pronoun that refers to the subject of the sentence. In this case, the subject is “he”, so the correct pronoun is “me”.
The other options are incorrect because they do not refer to the subject of the sentence. Option B, “her”, refers to the object of the sentence. Option C, “him”, also refers to the object of the sentence. Option D, “I”, is the subject of the sentence, but it is not in the correct form. The correct form of the pronoun “I” in the comparative form is “me”.