It is an long standing open problem that whether the scheme of commuting matrices is reduced. We suggest a way to tackle this problem via Langlands duality. In the introductory talk, we briefly recall the definition of commuting scheme, and how it is related to Ben-Zvi--Nadler's Betti Geometric Langlands (BGL) conjecture. In the research talk, we summarize recent progresses on BGL conjecture, and sketch a proof of reduceness of invariant function on commuting schemes, based on the conjecture in genus 1. This work is partially joint with David Nadler.