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AP EAMCET20226 Jul 2022Morning ShiftMathematicsMatricesActual

If A= [ array lll 1 & 1 & 3 1 & 7 & 9 2 & 3 & 7 array ] then Tr (A^2-A )=

Options

  1. A0
  2. B-12
  3. C152
  4. D125

Correct answer

C. 152

Step-by-step solution

Given A= [ array lll 1 & 1 & 3 1 & 7 & 9 2 & 3 & 7 array ] Now ( A ^2- A )= A ( A - I ) A^2-A= [ array lll 1 & 1 & 3 1 & 7 & 9 2 & 3 & 7 array ] ( [ array lll 1 & 1 & 3 1 & 7 & 9 2 & 3 & 7 array ]- [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] ) A^2-A= [ array lll 1 & 1 & 3 1 & 7 & 9 2 & 3 & 7 array ] [ array lll 0 & 1 & 3 1 & 6 & 9 2 & 3 & 6 array ] Thus Tr (A^2-A )= [ array ccc 7 & x & y a & 70 & Z b & c & 75 array ] aligned & =7+70+75 & =152 aligned

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