How to quickly tell this matrix is not rank 1?

Question

Is it possible to quickly evaluate the following matrix is rank 1 or not? \begin{pmatrix} 1 & -1 & -1 & 1 & 1 & 1 & -1 & -1 \\ -1 & 1 & -1 & -1 & 1 & 1 & 1 & -1 \\ -1 & -1 & 1 & -1 & -1 & 1 & 1 & 1 \\ 1 & -1 & -1 & 1 & -1 & -1 & 1 & 1 \\ 1 & 1 & -1 & -1 & 1 & -1 & -1 & 1 \\ 1 & 1 & 1 & -1 & -1 & 1 & -1 & -1 \\ -1 & 1 & 1 & 1 & -1 & -1 & 1 & -1 \\ -1 & -1 & 1 & 1 & 1 & -1 & -1 & 1 \end{pmatrix}

Answer 1

Similarly, if a matrix is of rank $1$, then its column/row space has dimension $1$, namely if you fix a column/row, all other columns/rows are scalar multiples of the fixed one.

Apparently, your new matrix is also not of rank $1$.

Answer 2

If a matrix is rank $1$, then each of its $2\times 2$ submatrices has zero determinant. However, the top left $2\times 2$ submatrix of your matrix has determinant $-1$. So, your matrix is not rank $1$.