Here the text is based on the corresponding reading in the King James Bible: “so he drove out the man” (Genesis 3:24). When Oliver Cowdery copied the text here from 𝓞 into 𝓟, he misread drove as drew. This reading has persisted in all the printed editions of the Book of Mormon. The critical text will restore the original, correct drove. The use of the verb drive here is supported by one other reference in the text to Adam and Eve being forced out of the garden of Eden: “and after that Adam and Eve had partaken of the forbidden fruit / they were driven out from the garden of Eden to till the earth” (2 Nephi 2:19).
Summary: In accord with the reading of the original manuscript, and in agreement with the corresponding King James language, restore the verb drove in Alma 42:2: “yea he drove out the man”.