a={a0,a1,a2}
b={b0,b1,b2}
c={c0,c1,c2}

aa={aa0,aa1,aa2}
bb={bb0,bb1,bb2}
cc={cc0,cc1,cc2}

aaa=Cross[a,aa]
bbb=Cross[b,bb]
ccc=Cross[c,cc]

podminkaO=Factor[Det[{aaa,bbb,ccc}]]

DD=Cross[Cross[a,b], Cross[aa,bb]]
EE=Cross[Cross[c,a], Cross[cc,aa]]
FF=Cross[Cross[b,c], Cross[bb,cc]]

podminkaDEF=Factor[Det[{DD, EE, FF}]]

Factor[podminkaDEF/podminkaO]

Det[{a,b,c}]