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MHT CET202123 Sep 2021Morning ShiftMathematicsMatricesActual

For a 3 3 matrix A, if A ( adj A )= [ array ccc -10 & 0 & 0 0 & -10 & 2 0 & 0 & -10 array ] , then the value of determinant of A is

Options

  1. A100
  2. B-1000
  3. C-10
  4. D20

Correct answer

C. -10

Step-by-step solution

aligned & We have | A ( adj A )|= [ array ccc -10 & 0 & 0 0 & -10 & 2 0 & 0 & -10 array ] & | A || adj A |=(-10)(100)=-1000 & | A || A |³⁻¹=-1000 | A |^3=-1000 | A |=-10 aligned

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