Consider a 9x9 matrix A. We say that A is a Sudoku matrix if it's the valid solution to a Sudoku puzzle. We require,
1) Every row and every column is a permutation of {1,2,3,4,5,6,7,8,9}.
2) If we write it in block form where Ai is a 3x3 matrix, then every Ai has elements {1,2,3,4,5,6,7,8,9}.

a) Find a Sudoku matrix with determinant 0.
b) Does there exist a Sudoku matrix with determinant 1. If not then determine the least positive number that a Sudoku matrix can have as a determinant.

Question

Consider a 9x9 matrix A. We say that A is a Sudoku matrix if it's the valid solution to a Sudoku puzzle. We require,
1) Every row and every column is a permutation of {1,2,3,4,5,6,7,8,9}. 
2) If we write it in block form where Ai is a 3x3 matrix, then every Ai has elements {1,2,3,4,5,6,7,8,9}.

a) Find a Sudoku matrix with determinant 0.
b) Does there exist a Sudoku matrix with determinant 1. If not then determine the least positive number that a Sudoku matrix can have as a determinant.

anonymous · Answer

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