Here $SU(3)$ is the set of all unitary matrices with ${\rm det}= 1$.
$$ \det \pmatrix{A_x & A_y & A_z \\B_x & B_y & B_z \\ C_x & C_y & C_z}=1, $$
whereas the triple product $C \cdot (A \times B)$ is
$$ \det \pmatrix{A_x & A_y & A_z \\B_x & B_y & B_z \\ C_x & C_y & C_z}=V. $$
Can we then connect $SU(3)$ to some set of $V$-preserving transformations?