How to find a 3x3 matrix with determinant =0 from which I can delete random column and random row to make it nonzero? I need to find a $3 \times 3$ matrix and the determinant of this matrix has to be $0$.
I also need to be able to delete randomly chosen column and row to make the determinant nonzero?  Is it even possible? Thank you.

The matrix
$$\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{pmatrix}$$works just fine : 


*

*the columns are in arithmetic progression, which means that the middle column is the arithmetic mean of the extremal columns, and thus they are not independent.

*for any $2\times 2$ submatrix, the difference of the columns is a multiple of $\left(\begin{smallmatrix}1\\ 1 \end{smallmatrix}\right)$, but none of the column is, so the columns must generate a space of dimension $2$, hence they are linearly independent.

