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AP EAMCET202124 Aug 2021Evening ShiftMathematicsMatricesActual

Let A be a 2 2 matrix with real entries. Let I be the 2 2 identity matrix. Tr (A) denotes the sum of diagonal entries of A . Assume that A^2=I Statement I If A I and A -1 , then det A=-1 Statement II If A I and A -1 , then Tr A 0

Options

  1. AStatement I is true, statement II is true, statement II is a correct explanation for statement I
  2. BStatement I is true, statement II is true, statement II is not a correct explanation for statement I
  3. CStatement I is true, statement II is false
  4. DStatement I is false, statement II is true

Correct answer

C. Statement I is true, statement II is false

Step-by-step solution

Let A= [ array ll 0 & 1 1 & 0 array ]A^2= [ array ll 0 & 1 1 & 0 array ] [ array ll 0 & 1 1 & 0 array ]= [ array ll 1 & 0 0 & 1 array ]=I Here, A^2=I,|A|=-1 and A I Tr (A)=0 Statement I is true. Statement II is false.

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