The correct option is A −2
Δ=∣∣
∣
∣∣(a+1)(a+2)a+21(a+2)(a+3)a+31(a+3)(a+4)a+41∣∣
∣
∣∣
Applying C1→C1−C2,
Δ=∣∣
∣
∣∣(a+2)aa+21(a+3)(a+1)a+31(a+4)(a+2)a+41∣∣
∣
∣∣
Applying C2→C2−C3,
Δ=∣∣
∣
∣∣(a+2)aa+11(a+3)(a+1)a+21(a+4)(a+2)a+31∣∣
∣
∣∣
Applying R2→R2−R1 and R3→R3−R1,
Δ=∣∣
∣∣a2+2aa+112a+3104a+820∣∣
∣∣=6−8=−2