Nullspace(A) mod p computes a basis for the null space (Nullspace) of the linear transformation defined by the matrix A. The result is a (possibly empty) set of vectors.

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,3\right]\,\left[1\,2\,3\right]\,\left[0\,0\,0\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 3\\ 1& 2& 3\\ 0& 0& 0\end{array}\right]$

$\mathrm{Nullspace}\left(A\right)\mathbf{mod}5$

$\left\{\left[\begin{array}{c}3\\ 1\\ 0\end{array}\right]\,\left[\begin{array}{c}2\\ 0\\ 1\end{array}\right]\right\}$