Question 140626
A matrix of the form
({{{matrix(3,3,
A[1],A[2],A[3],
B[1],B[2],B[3],
C[1],C[2],C[3])}}})
has a determinant,D, equal to
{{{D=A[1]*(B[2]*C[3]-B[3]*C[2]) + A[2]*(B[3]*C[1]-B[1]*C[3]) + A[3]*(B[1]*C[2]-B[2]*C[1])}}}

{{{D=4*(1*(-3)-(-2)*(-4)) + (-4)*((-2)*(-2)-(-1)*(-3)) + 10*((-1)*(-4)-1*(-2))}}}
{{{D=4*(-3-8) + (-4)*(4-3) + 10*(4+2)}}}
{{{D=-44 + (-4) + 60}}}
{{{D=12}}}