With that many unknowns I am astonished that this completes in reasonable time. {{{a,b,c},{d,e,f},{g,h,i}},{{j,k,l},{m,n,o},{p,q,r}}}/. FindInstance[{{a,b,c},{d,e,f},{g,h,i}}.{{j,k,l},{m,n,o},{p,q,r}}== {{0,0,0},{0,0,0},{0,0,0}}&&Element[a|b|c|d|e|f|g|h|i|j|k|l|m|n|o|p|q|r,Reals], {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r},3] All the results I've seen have rational or integer entries