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It is proven that every geometric lattice of finite rank greater than 1 has amatching between the points and hyperplanes. This answers a question of P\'olyaPrize-winner Anders Bj\"orner from the 1981 Banff Conference on Ordered Sets,which he raised as a "challenging question" in 1976.

A "Challenging Question" of Bj\"orner from 1976: Every Infinite Geometric Lattice of Finite Rank Has a Matching