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If it can be ascertained experimentally that the 3X3 Majorana neutrino massmatrix M_nu has vanishing determinants for one or more of its 2X2 submatrices,it may be interpreted as supporting evidence for the theoretically well-knowncanonical seesaw mechanism. I show how these two things are connected and offera realistic M_nu with two zero subdeterminants as an example.Comment: title changed, version to appear in PRD(RC

Connection between the neutrino seesaw mechanism and properties of the Majorana neutrino mass matrix