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NDA2013MathematicsDeterminantsActual

If D is a determinant of order 3 and D^ is the determinant obtained by replacing the elements of D by their cofactors, then which one of the following is correct?

Options

  1. AD^ =D^2
  2. BD ^ = D ^3
  3. CD ^ =3 D ^2
  4. DD ^ =3 D ^3

Correct answer

A. D^ =D^2

Step-by-step solution

aligned & D ^ = cofactor D & | D ^ |= cofactor D & | D ^ |=| D |³⁻¹ & | D ^ |=| D |^2 aligned So D ^ = D ^2

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