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JEE Main2016MathematicsMatricesActual

If A = - 4 - 1 3 1 , then the determinant of the matrix A 2016 - 2 A 2015 - A 2014 is :

Options

  1. A- 175
  2. B2014
  3. C2016
  4. D- 25

Correct answer

D. - 25

Step-by-step solution

A = - 4 - 1 3 1 ⇒     A 2 = - 4 - 1 3 1   - 4 - 1 3 1 = 13 3 - 9 - 2 and A =- 1 Now, A 2016 - 2 A 2015 - A 2014 = A 2014   A 2 - 2 A - I ⇒ A 2016 - 2 A 2015 - A 2014 = A 2014   A 2 - 2 A - I   A 2 - 2 A - I = 20 5 - 15 - 5 = A 2014   20 5 - 15 - 5 = - 25

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