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In 1951 A. M. Ostrovskii published the remarkable theorem being the far generalization of the known J. Hadamard theorem concerning the matrix with the diagonal predomination [3]. The mentioned Ostrovskii result is the following. Let A = (aij ) be the square matrix of the order n. Let for a certain value of the parameter α, 0 p1−α i q i , i = 1,2, . . . ,n, (1)

Estimates of determinants and of the elements of the inverse matrix under conditions of Ostrovskii theorem