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BITSAT2015MathematicsMatricesActual

Let M bea 3 3 n n -singular matrix with det ( M )= . If [ M ⁻¹ . adj ( adj ( M )]= KI , then the value of K is

Options

  1. A1
  2. B²
  3. C³

Correct answer

B. ²

Step-by-step solution

We know that, M( adj M)=|M| I Replacing M by adj M , we get adj M[ adj ( adj M)= det ( adj M) I= det (M) M⁻¹ [ adj ( adj M)= ² 1 . [ M ⁻¹= 1 | M | adj ( M ) ] M ⁻¹[ adj ( adj M)]= ² I M ⁻¹[ adj ( adj M )]= I But M⁻¹[ adj ( adj M)]=K I Hence, K =

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