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AP EAMCET202421 May 2024Evening ShiftMathematicsMatricesActual

If 3 A= [ array ccc 1 & 2 & 2 2 & 1 & -2 a & 2 & b array ] and A A^ T =I , then a b + b a

Options

  1. A- 5 2
  2. B13 6
  3. C- 13 6
  4. D5 2

Correct answer

D. 5 2

Step-by-step solution

(3 A)(3 A)^T= [ array ccc 1 & 2 & 2 2 & 1 & -2 a & 2 & b array ] [ array ccc 1 & 2 & a 2 & 1 & 2 2 & -2 & b array ] aligned & 9 A A^T= [ array ccc 9 & 0 & a+4+2 b 0 & 9 & 2 a+2-2 b a+2 b+4 & 2 a+2-2 b & a^2+4+b^2 array ] & a+2 b+4=0 and 2 a+2-2 b=0 & a=-2, b=-1 a b + b a =2+ 1 2 = 5 2 . aligned

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