A={{a,e,s},{b,o,d},{u,i,m}}; S=Flatten[A];
f[R_]:=Partition[R,3]; U=Permutations[S]; V=Map[f,U];
Do[Print[U[[k]],"   ",Det[V[[k]]]],{k,Length[V]}]

    | a e s |
    | o i u |
    | d t m |

  m i a  + d e u  +  s o t  -t u a  -d i s - e m o