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A = (aij) ∈ Rn×n is called anti-bisymmetric matrix if aij＝-aij,aij =-an-j+1,,n-i+1,i ,j＝1,2,… ,n. We denoted the set of all n × n anti-bisymmetric ma-trices by ABSRin×n. In this paper, we discuss the following two problems:Problem I: Given