Question

Construct a square matrix A of order 3

Answer 1

`A_(ij)` refers to the entry of
`A` in row
`i` and column
`j`.

When
`i=j`, the entry in question lies on the diagonal. In this case,
`A_(ij)=0` so

`A = \begin{bmatrix} 0 & \square & \square \\ \square & 0 & \square \\ \square & \square & 0 \end{bmatrix}`

When
`i<j`, the row number is smaller than the column number, which happens for each
`A_(ij)` in the upper half of
`A`.

`A = \begin{bmatrix} 0 & -1 & -1 \\ \square & 0 & -1 \\ \square & \square & 0 \end{bmatrix}`

When
`i>j`, the row number is larger, which happens everywhere else in the matrix.

`A = \begin{bmatrix} 0 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & 1 & 0 \end{bmatrix}`