Maximum determinant of matrix with only 1 and -1 elements?

[mvgmonteiro]

1. The problem statement:
Find out the maximum determinant of a matrix nxn which have just 1 and -1 elements.

2. The attempt at a solution:
I have tried for 2x2 and 3x3 matrices and so generalizing for nxn matrices. But I can’t figure out any pattern or something like that. Also, I barely know about the Leibniz Formula for Determinants, and don’t think so that it is helpful here. Thus, I am just stucked at that problem, and don’t have any great idea so far..

 

[fresh_42]

1. The problem statement:
Find out the maximum determinant of a matrix nxn which have just 1 and -1 elements.

2. The attempt at a solution:
I have tried for 2x2 and 3x3 matrices and so generalizing for nxn matrices. But I can’t figure out any pattern or something like that. Also, I barely know about the Leibniz Formula for Determinants, and don’t think so that it is helpful here. Thus, I am just stucked at that problem, and don’t have any great idea so far..

I don't know what the Leibniz formula is in this context. But how is a determinant defined? What do you work with?