[tex]A_{ij}[/tex] refers to the entry of [tex]A[/tex] in row [tex]i[/tex] and column [tex]j[/tex].
When [tex]i=j[/tex], the entry in question lies on the diagonal. In this case, [tex]A_{ij}=0[/tex] so
[tex]A = \begin{bmatrix} 0 & \square & \square \\ \square & 0 & \square \\ \square & \square & 0 \end{bmatrix}[/tex]
When [tex]i<j[/tex], the row number is smaller than the column number, which happens for each [tex]A_{ij}[/tex] in the upper half of [tex]A[/tex].
[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ \square & 0 & -1 \\ \square & \square & 0 \end{bmatrix}[/tex]
When [tex]i>j[/tex], the row number is larger, which happens everywhere else in the matrix.
[tex]A = \begin{bmatrix} 0 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & 1 & 0 \end{bmatrix}[/tex]
