• |1 x(x+1) x+1; 1 y(y+1) y+1; 1 z(z+1) z+1|
• B|1 x+1 x²+1; 1 y+1 y²+1; 1 z+1 z²+1|
• C|0 x−y x²−y²; 0 y−z y²−z²; 1 z z²|
• D|2 x+y x²+y²; 2 y+z y²+z²; 1 z z²|

Let the original determinant D have columns C1=(1,1,1), C2=(x,y,z), C3=(x²,y²,z²). Option A's columns are C1, C2+C3, C1+C2 — expanding by multilinearity, all terms vanish except det(C1,C3,C2), which equals −D (columns 2 and 3 swapped). Option B's columns are C1, C1+C2, C1+C3, which reduces to exactly D. Options C and D are the original matrix's rows combined via valid elementary row operations (R1−R2, R2−R3 for C; R1+R2, R2+R3 for D), which never change a determinant's value, so both equal D. Only option A does NOT equal the original determinant D (it equals −D instead).