Adam Clarke on Deuteronomy 31:9

Moses wrote this law - Not the whole Pentateuch, but either the discourses and precepts mentioned in the preceding chapters, or the book of Deuteronomy, which is most likely.

Some of the rabbins have pretended that Moses wrote thirteen copies of the whole Pentateuch; that he gave one to each of the twelve tribes, and the thirteenth was laid up by the ark. This opinion deserves little credit. Some think that he wrote two copies, one of which he gave to the priests and Levites for general use, according to what is said in this verse, the other to be laid up beside the ark as a standard copy for reference, and to be a witness against the people should they break it or become idolatrous. This second copy is supposed to be intended Deu 31:26. As the law was properly a covenant or contract between God and the people, it is natural to suppose there were two copies of it, that each of the contracting parties might have one: therefore one was laid up beside the ark, this was the Lord's copy; another was given to the priests and Levites, this was the people's copy.