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Is it possible to construct a matrix with 5*5 cells, where the value in each cell is taken from the set {-2,-1,0,1,2}, such that all of the 12 sums of the cells in each row/column/main diagonal have different values (5 sums of matrix's rows, 5 sums of the matrix's columns, and 2 sums of the main diagonals)?

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Assuming I haven't missed something, this appears to work

enter image description here

I started by just putting -2 in the top row. The sum is -10, so I made the first column sum to a different number -9. I repeated this pattern until the diagonal was completed. The sum of the diagonal (bottom left to top right) was -5, so I skipped -5 and continued with -4. The remaining few cells were trivial to select to have different numbers.

To assist in ensuring I didn't miss a number, I applied conditional formatting to the sum cells in Excel so that they would be highlighted red if a value was duplicated.

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