An incline S is a commutative semiring satisfying the condition s + 1 = 1 for all s ∈ S. It is proved that an n × n matrix A over an incline S is invertible if and only if ∑nk=1 aik = 1(i = 1, 2,…, n) and aikajk = 0(i ≠ j, k = 1, 2,…, n).Complements can be defined in an incline S and it is obtained that every invertible matrix over S is a permutation matrix if and only if S does not contain elements, distinct from 0 and 1, having a complement.%坡S是一个元素满足条件s+1=1的交换半环.证明了坡S上n×n矩阵A可逆当且仅当∑nk=1 aik=1(i=1,2,…,n)且aikajk=0(i≠j,k=1,2,…,n).在坡S中可定义补元,得到S上每一个可逆矩阵是一个置换矩阵当且仅当S不包含不同于0和1的有补元.
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