24 And, notwithstanding we believe in Christ, we the law of Moses, and look forward with steadfastness unto Christ, until the law shall be fulfilled.
25 For, for this end was the given; wherefore the law hath become unto us, and we are made alive in Christ because of our faith; yet we keep the law because of the commandments. (2 Nephi 25)
This post explains that the oft-repeated 'Book of Mormon proverb', is a reference to the Mosaic covenant. When a term is used as a key word or phrase to reference a longer text, it is called metalepsis. This is an appropriate description of "inasmuch as ye shall keep my commandments, ye shall prosper in the land". It invokes the entire Mosaic covenant. A related phrase that I have found is the "judgments, statutes and commandments" of God. This is also a metalepsis referring to the terms and conditions of the Mosaic covenant for the people of Israel. All that they are asked to do to become a "peculiar nation" (Deuteronomy 26:18) and God's chosen covenant people is laid out in the books of Exodus to Deuteronomy. It is summarized by his "judgments, statutes and commandments". For instance:
In that I command thee this day to love the Lord thy God, to in his ways, and to keep his commandments and his statutes and his , that thou mayest live and multiply: and the Lord thy God shall bless thee in the land whither thou goest to possess it. (Deuteronomy 30:16)
The Nephite term, "prosper in the land" is a summary of "live and multiply" and "the Lord thy God shall bless thee in the land" and other covenant promises scattered around in the Torah, especially in Deuteronomy. But the "keep the commandments" part of the Book of Mormon proverb is also short for the commandments, statutes and judgments, even though all three are also mentioned at times in the Book of Mormon. The order of those three terms varies and sometimes only one or two of the three are used, but I don't know if that has significance. They are repeated multiple times in the Book of Deuteronomy, usually to summarize and refer to all the detailed instructions that Israel have received through Moses. Here are a couple more examples
Now these are the commandments, the , and the , which the Lord your God commanded to teach you, that ye might do them in the land whither ye go to possess it (Deuteronomy 6:1)
Therefore thou shalt the Lord thy God, and keep his , and his statutes, and his , and his commandments, alway. (Deuteronomy 11:1)
These are only a few examples but Deuteronomy is saturated with this language. These expressions are also used when explaining why Israel have lost wars and ultimately been taken captive by the Babylonians.
And ye shall know that I am the Lord: for ye have not walked in my statutes, neither executed my , but have done after the of the that are round about you. (Ezekiel 11:12)
In the Book of Mormon, this expression seems to be used to inform the reader that the broken off branch of the House of Israel in a promised land were keeping their part of the covenant. This is how Nephi puts it
10 And we did observe to keep the judgments, and the , and the commandments of the Lord in all things, according to the of Moses.
11 And the Lord was with us; and we did exceedingly; for we did sow seed, and we did reap again in abundance. And we began to raise flocks, and herds, and animals of every kind. (2 Nephi 5)
Nephi clearly attributes their abundant reaping and increase of flocks to the fact that they kept the terms of the Mosaic covenant. Prospering in the land was the promise. They had kept their part and the Lord always keeps his. Another similar example
Nevertheless did fill the judgment-seat with justice and equity; yea, he did observe to keep the statutes, and the judgments, and the commandments of God; and he did do that which was right in the sight of God continually; and he did walk after the ways of his father, insomuch that he did prosper in the land. (Helaman 3:20)
At this point, several hundred years have passed since Lehi and his family left Jerusalem, but the Nephites obviously remember the covenant of their fathers, the covenant terms and the Lord's promises that are still in effect. It is also interesting to note that the terms and blessings of the Mosaic covenant applied on an individual level as well as collectively. "he [Helaman] did prosper in the land".
Several times, this expression is used about Lamanite converts. The Book of Mormon stresses that true conversion at the time before Christ included keeping the Law of Moses. This is how they became covenant people. But unlike the Deuteronomists of old, it also included looking forward to Christ and his redemption, like Nephi expressed in the first verse I quoted.
14 And they did also their weapons of war, according as their brethren had, and they began to be a righteous people; and they did walk in the ways of the Lord, and did observe to keep his commandments and his statutes.
15 Yea, and they did keep the law of Moses; for it was expedient that they should keep the law of Moses as yet, for it was not all fulfilled. But notwithstanding the of Moses, they did look forward to the coming of Christ, considering that the law of Moses was a of his coming, and believing that they must keep those until the time that he should be revealed unto them.
16 Now they did not suppose that came by the of Moses; but the law of Moses did serve to strengthen their faith in Christ; and thus they did retain a through faith, unto eternal salvation, relying upon the spirit of prophecy, which spake of those things to come. (Alma 25)
Like Nephi, they kept the law of Moses because of the commandments. Those were the covenant terms and source of their blessings. But it was also the pointer towards Christ, the ultimate source of blessings and prosperity, even "eternal salvation".