A Public Problem about Inverse M-matrices

M. Neumann in gave a public problem. For an ntimesn inverse M -matrix A, the Hadamard product AdegA is an inverse of M -matrix. They have checked the conjecture without failure on many examples. So far, the conjecture has not been proved. In the paper, we present a different class inverse M - matrix and investigate the Hadamard product AdegA and AdegB are closed. If A and any A_i(i=1,2,middotmiddotmiddotN-1,N) are inverse M - matrices, we also check a more general conjecture that for any pges1, the Hadamard power Adeg^p=(a_ij ^p) , Adeg^infin = (a_ij ^infin) and the Hadamard multiplication A₁degA₂degA₃degmiddotmiddotmiddotdegA_N are closed.