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Question

If Δ = ∣ ∣a1b1c1a2b2c2a3b3c3∣ ∣ and A1, B1, C1 denote the co-factors of a1, b1, c1 respectively, then the value of the determinant ∣ ∣A1B1C1A2B2C2A3B3C3∣ ∣ is
  1. Δ2
  2. Δ
  3. Δ3
  4. 0


Solution

The correct option is A Δ2
We know that ΔΔ = ∣ ∣a1b1c1a2b2c2a3b3c3∣ ∣ ∣ ∣A1B1C1A2B2C2A3B3C3∣ ∣
=∣ ∣ ∣ a1A1000 a2A2000 a3A3∣ ∣ ∣ = ∣ ∣Δ000Δ000Δ∣ ∣ = Δ3 Δ = Δ2.

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