Galatians 3:11

by the law--Greek, "IN the law." Both in and by are included. The syllogism in this verse and Gal 3:12, is, according to Scripture, "The just shall live by faith." But the law is not of faith, but of doing, or works (that is, does not make faith, but works, the conditional ground of justifying). Therefore "in," or "by the law, no man is justified before God" (whatever the case may be before men, Rom 4:2) --not even if he could, which he cannot, keep the law, because the Scripture element and conditional mean of justification is faith. The just shall live by faith-- (Rom 1:17; Hab 2:4). Not as BENGEL and ALFORD, "He who is just by faith shall live." The Greek supports English Version. Also the contrast is between "live by faith" (namely, as the ground and source of his justification), and "live in them," namely, in his doings or works (Gal 3:12), as the conditional element wherein he is justified.

— Jamieson-Fausset-Brown Commentary (public domain)