Comment by toAnswerIt

to see it consider this:

S = 1 + 2 + 3 + ... + n-1 + n

+

S = n + n-1 + n-2 + ...+ 2 + 1

=

2S = n+1 + n+1 + n+1 + ... + n+1 + n+1

every column sums to n+1