matrix = {{0, 3, 1, 7, 5, 9, 8, 6, 4, 2}, {7, 0, 9, 2, 1, 5, 4, 8, 6,
    3}, {4, 2, 0, 6, 8, 7, 1, 3, 5, 9}, {1, 7, 5, 0, 9, 8, 3, 4, 2,
    6}, {6, 1, 2, 3, 0, 4, 5, 9, 7, 8}, {3, 6, 7, 4, 2, 0, 9, 5, 8,
    1}, {5, 8, 6, 9, 7, 2, 0, 1, 3, 4}, {8, 9, 4, 5, 3, 6, 2, 0, 1,
    7}, {9, 4, 3, 8, 6, 1, 7, 2, 0, 5}, {2, 5, 8, 1, 4, 3, 6, 7, 9,
    0}};
Damm[num_Integer] := Module[{row},
  row = 0;
  Do[
   row = matrix[[row + 1, d + 1]]
   ,
   {d, IntegerDigits[num]}
   ];
  row == 0
  ]
Damm /@ {5724, 5727, 112946}