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AP EAMCET2006MathematicsMatrices

A= [ array lll 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 array ] then A^3-4 A^2-6 A is equal to :

Options

  1. A0
  2. BA
  3. C-A
  4. DI

Correct answer

C. -A

Step-by-step solution

A= [ array lll 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 array ] A^2= [ array lll 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 array ] [ array lll 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 array ]= [ array lll 9 & 8 & 8 8 & 9 & 8 8 & 8 & 9 array ]A^3=A^2 A= [ array lll 9 & 8 & 8 8 & 9 & 8 8 & 8 & 9 array ] [ array lll 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 array ]= [ array lll 41 & 42 & 42 42 & 41 & 42 42 & 42 & 41 array ] A^3-4 A^2-6 A= [ array lll 41 & 42 & 42 42 & 41 & 42 42 & 42 & 41 array ]-4 [ array lll 9 & 8 & 8 8 & 9 & 8 8 & 8 & 9 array ]-6 [ array lll 1

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