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In this paper we give a proof that the largest set of perfect matchings, inwhich any two contain a common edge, is the set of all perfect matchings thatcontain a fixed edge. This is a version of the famous Erd\H{o}s-Ko-Rado theoremfor perfect matchings. The proof given in this paper is algebraic, we firstdetermine the least eigenvalue of the perfect matching derangement graph anduse properties of the perfect matching polytope. We also prove that the perfectmatching derangement graph is not a Cayley graph.

An algebraic proof of the Erd\H{o}s-Ko-Rado theorem for intersecting families of perfect matchings