Question 1028695
If A is a nxn skew symmetric matrix, then {{{-A = A^t}}}.

Let A have main diagonal elements of {{{a[11]}}}, {{{a[22]}}}, {{{a[33]}}}, ...,{{{a[nn]}}}.
If the transpose of A is obtained, then the position of the main diagonal elements are preserved, because they are the pivot elements. Since the transpose of A is supposed to be equal to -A, this means that the main diagonal elements {{{-a[11]}}}, {{{-a[22]}}}, {{{-a[33]}}}, ...,{{{-a[nn]}}} of -A must be equal to {{{a[11]}}}, {{{a[22]}}}, {{{a[33]}}}, ...,{{{a[nn]}}}.

==> {{{a[11] = -a[11]}}} ==> {{{a[11] = 0}}},
{{{a[22] = -a[22]}}} ==> {{{a[22] = 0}}},
{{{a[33] = -a[33]}}} ==> {{{a[33] = 0}}},...
{{{a[nn] = -a[nn]}}} ==> {{{a[nn] = 0}}}.

Therefore, the main diagonal elements of A are all 0.