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I have an 15*15 matrix and its determinant is equal to zero. I want to switch columns or/and rows in order to make its determinant non-zero. Is it possible? Here is the matrix

1,  0,  0,  1,  2,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0;
1,  1,  1,  0,  0,  0,  1,  0,  2,  0,  0,  0,  0,  0,  0;
1,  0,  0,  0,  0,  0,  1,  1,  2,  0,  0,  0,  0,  0,  0;
1,  1,  0,  1,  0,  0,  0,  0,  0,  0,  0,  1,  0,  1,  0;
2,  0,  0,  0,  0,  0,  0,  2,  0,  1,  0,  0,  0,  0,  0;
2,  2,  2,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0;
2,  0,  0,  2,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0;
3,  3,  3,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  0,  0;
0,  1,  1,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  2;
0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  3;
1,  0,  0,  1,  4,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0;
1,  1,  1,  1,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0;
0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  0,  2,  0;
0,  2,  2,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0;
0,  1,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  1,  0,  0
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I have an 15*15 matrix and its determinant is equal to zero. I want to switch columns or/and rows in order to make its determinant non-zero. Is it possible?

It's impossible: swapping two columns (or rows) only changes the sign of the determinant.

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