Matrices permutable to ∗ matrices

AbstractA (0, 1) matrix (aij) is said to be a ∗ matrix iff aij = 1 implies ai′j′ = 1 for all (i′, j′) satisfying 1 ⩽ i′ ⩽ i, 1 ⩽ j′ ⩽ j. (0, 1) matrices permutable to ∗ matrices are characterized and counted. Commutivity of matrices which permute to ∗ matrices is also discussed