41CL Quiz: Determinant of 30x30 anti-Identity matrix

[hibiki]

I see that the solution is 29 or -29 depending on whether the diagonal of 0's is descending from left to right or ascending. But my curiosity is why a simple sum or subtraction of a string of 1's (integers) multiplied 29 times and accumulated 29 times resulted in a non integer number in some responses.