Determinant of the Minimum and Maximum of the Row and Column Number

We prove that the determinant of the matrix whose entries are the minimum of the row and column number is one. We also prove that the determinant of the determinant whose entries are the maximum of the row and the column number is n*(-1)^(n-1) by induction. In both arguments we use the row and column reduction properties of matrices to simplify the calculations.
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