LetA=M-NbearegularsplittingofanM-matrix.WestudythespectralpropertiesoftheinerationmatrixM-1N.UnderamildassumptiononM-1N.somenecessaryandsufficentconditionssuchthatp(M-1N)=1areobtainedandthealgebraicmultiplicityandtheindexassociatedwitheigenvalue1inM-1Nareconsidered.