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AP EAMCET202123 Aug 2021Evening ShiftMathematicsDeterminantsActual

If A( )= [ array cc i & & i array ] is a matrix, where i= -1 , then which of the following is not true

Options

  1. Adet A( + )= det A(- )
  2. Bdet A(- )= det A( )
  3. Cdet [A( )]⁻¹=1
  4. Ddet A(- )=-1

Correct answer

C. det [A( )]⁻¹=1

Step-by-step solution

A( )= [ array cc i & & i array ] where i= -1 |A( )|=i^2 ^2 - ^2 =- ( ^2 + ^2 )=-1 adj A( )= [ array cc i & - - & i array ] (A( ))⁻¹= 1 -1 [ array cc i & - - & i array ] |A( )⁻¹ |=- i^2 ^2 - ^2 aligned & =- (- ^2 - ^2 ) & =-(-1)=1 aligned

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