Definition contraction a b k := k *: (b - a) + a.

Lemma col_2D_aux_1 a b c :
((a 0 1 - c 0 1) * (b 0 0 - c 0 0) == (a 0 0 - c 0 0) * (b 0 1 - c 0 1)) =
((a 0 0 - b 0 0) * (b 0 1 - c 0 1) == (a 0 1 - b 0 1) * (b 0 0 - c 0 0)).