Compute the determinant of the matrix

(ie. all diagonal entries equal to zero, all above diagonal entries equal to 1, all below diagonal entries equal to -1)

I am not sure how to go about finding this in general. I have found that the determinants when is 1 and 2 are both 1, but that doesn't really help me in general, and I don't really have any idea what to start with for the general case. Any tips?