Trouble understanding αὐτῷ

Hi, I’m currently working my way through From Alpha to Omega by Anne Groton. I’m currently at chapter 14 on personal pronouns and dative of possessions.

In the exercise of translating from English to Greek, there is one sentence I have trouble translating:

I myself have that man’s cloak, but do you yourselves have this woman’s books?

My attempt is as follows:

αὐτὸς μὲν τὸν ἐκεινου ἱματιον ἔχω, αὐτὸς δὲ τὰ τούτου βιβλία ἔχεις;

However, the answer key gives:

ἐμοὶ μὲν > αὐτῷ > τὸ ἱμάτιόν ἐστιν, ὑμῖν > αὐτοῖς > τὰ βιβλία ἐστιν;

At first I thought this is a case of dative of possessions: nominative + dative + third person of εἰμὶ. So, that man’s cloak and this woman’s books are the nominatives, ἐμοὶ (to me) and ὑμῖν (to you) indicates whom the things belong to.

However, if the sentence is in dative of possessions form, what does αὐτῷ and αὐτοῖς mean in this case? Both are in dative and masculine form. However, the former is in singular form and the latter in plural form. My guess is that these mean “myself and yourselves” respectively. However, the book says that αὐτὸς means “-self” if it is in nominative form, or modifying an expressed noun in predicate position. So, since both are not in nominative form, I rule out -self in this case.

Also, both words do not modify the noun, as the cases do not match with the nouns: τὸ ἱμάτιόν and τὰ βιβλία are in nominative form.

So, what does αὐτῷ and αὐτοῖς mean in this case?

Please help me as I’m confused. Thanks.

I think that you did not notice that the subject of the second sentence is plural (yourselves, not yourself). So the book is right but, if you want to use ἔχω, then you should use the second person plural.
Also, this [woman] should be feminine. Why don’t you give it another try?

I

αὐτός-ή-ό can also mean self when it’s in agreement with a substantive (predicate position) or a personal pronoun.
So in the sentence from the answer key, αὐτῷ agrees with ἐμοί and αὐτοῖς agrees with ὑμῖν. Since we don’t know the gender of ὑμῖν, I believe the default gender is masculine. The dative of possessor would be perfect in this case, because the cloak and the books actually belong to someone else, and the dative of possessor indicates temporary possession.

EDIT: I just found Chapter 14 of your textbook in the preview pages on Amazon and the statement you’re referring to goes like this: “If you see a form of αὐτός in the nominative case, it cannot be the third person pronoun; it must mean “-self” or (in the attributive position) “same”.” That doesn’t mean you can’t use it to mean “self” in the other cases. It just has to be in the predicate position, e.g. τῷ αὐτῷ φίλῷ = to the same friend (attributive position) αὐτῷ τῷ φίλῷ = to the friend himself (predicate position)

Thank you, I think this was the gap in my understanding.