NDA 2025 · PYQ · Determinants / Cofactors · medium
If Δ = |a b c; d e f; g h i| and A, B, C, D, G are the cofactors of the elements a, b, c, d, g respectively, then what is bB + cC - dD - gG equal to?
- A.0✓ Correct
- B.1
- C.Δ
- D.-Δ
The expansion of Δ along row 1 gives aA + bB + cC = Δ. Expansion along column 1 gives aA + dD + gG = Δ. So bB + cC = Δ - aA and dD + gG = Δ - aA. Therefore bB + cC - dD - gG = (Δ - aA) - (Δ - aA) = 0.
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