I had a question about computing determinants and just was wondering what was allowed. So I know that for an n x n matrix, you can go across a row and choose the matrix element as your determinant coefficient for the (n-1) x (n-1) determinant and you go across the row and do this until you're finished with the row. I also know that this process is recursive until you get down to 2x2 from which point you work your way out of this nested maze of determinants you've created for yourself and found the determinant. I also know that you can go down a column and use its matrix elements as coefficients instead of going down the row. This is useful if there are more zeros down the column than across the row and it simplifies the calculation. I am aware that the sign of the coefficient depends on its location in the matrix. The top left element is positive and the rest of the signs are arranged like a checkerboard; no same signs have edges touching. What I wanted to know is, if instead of using the rows or columns as the coefficients for your lower order determinants, could you use diagonals? If you got the signs correct, cancelled out the row and column that it's in and used the remaining matrix elements for your lower order matrix. Could you do this to find the determinant? I do realize that if you used the diagonal, all the coefficients would have the same sign. But does this matter? Is this against the rules? As long as every row or every column is represented, it shouldn't matter right? Or is that incorrect?