Let Pnr be the set of n-by-n r-regular primitive (0, 1)-matrices. In this paper we find an explicit formula in terms of n and r for the minimum exponent achieved by matrices in Pnr. Moreover, we give matrices achieving that exponent. Gregory and Shen [6] conjectured that bnr = n r 2 +1 is an upper bound for the exponent of matrices in Pnr. We present… (More)