Try to generate a random matrix modulo m using, say, examples from the ?LinearAlgebra,Modular,Random help page.

with(LinearAlgebra[Modular]):
A1 := Random(31,5,4,integer[]);

                             [0    0    0    0]
                             [                ]
                             [0    0    0    0]
                             [                ]
                       A1 := [0    0    0    0]
                             [                ]
                             [0    0    0    0]
                             [                ]
                             [0    0    0    0]

A2 := Random(31,20,30,float[8],Fortran_order);
                          [ 20 x 30 Matrix       ]
                    A2 := [ Data Type: float[8]  ]
                          [ Storage: rectangular ]
                          [ Order: Fortran_order ]

> A2[1..10,1..10];

          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]
          [                                               ]
          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]
          [                                               ]
          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]
          [                                               ]
          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]
          [                                               ]
          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]
          [                                               ]
          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]
          [                                               ]
          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]
          [                                               ]
          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]
          [                                               ]
          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]
          [                                               ]
          [0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0.]

A3 := Random(31,3,0,integer[]);

                                    [0]
                                    [ ]
                              A3 := [0]
                                    [ ]
                                    [0]

A4 := Random(31,0,5,float[8]);

                      A4 := [0., 0., 0., 0., 0.]

All zeros.

Alec