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Let A=||ai,j || be an n x n matrix consisting of non-negative elements. It is well known [1, p. 463] that A is primitive if and only if, for some positive integer n, An has all its elements positive. One needs to know only this property of primitive matrices to understand this paper. If Ak is positive (i.e. has all its elements positive), then Ah is also positive for all  integers h>k [1, p. 463]. 2 Letting A be primitive, we shall define γ(A) as the smallest positive integer h such that Ah is positive.