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AP EAMCET202418 May 2024Morning ShiftMathematicsMatricesActual

If the determinant of a 3^ rd order matrix A is K , then the sum of the determinants of the matrices (A A^T ) and (A-A^T ) is

Options

  1. A2K
  2. B0
  3. CK ^2
  4. DK

Correct answer

C. K ^2

Step-by-step solution

Given, A is 3 3 matrix and | A |= k Now, A - A ^ T is always a skew symmetric matrix of order 3 So, | A - A ^ T |=0 and | AA ^ T |=| A | | A ^ T |= K K = K ^2 So, | AA ^ T |+ | A - A ^ T |= O + K ^2= K ^2

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