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AP EAMCET202318 May 2023Morning ShiftMathematicsMatricesActual

If A and B are non-singular matrices and det ( AB )=( det A )( det B ) , then (( det A )( det B )) B ⁻¹ ~A ⁻¹=

Options

  1. AAdj (BA)
  2. BAdj ( A )+ Adj ( B )
  3. CAdj ( AB )
  4. D( Adj B)( Adj A)

Correct answer

C. Adj ( AB )

Step-by-step solution

det (A B)=( det A) ( det B) Now, ( det A)( det B)) B⁻¹ A⁻¹=( det (A B))(A B)⁻¹= Adj ( AB ) ( A ⁻¹= Adj ( A ) det ( A ) )

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