If $ A=\left[\begin{array}{cc}-4 & -1 \ 3 & 1\end{array}\right] $, then the determinant of the matrix $ \left(A^{2016}-2 A^{2015}-A^{2014}\right) $ is

Question

If $ A=\left[\begin{array}{cc}-4 & -1 \ 3 & 1\end{array}\right] $, then the determinant of the matrix $ \left(A^{2016}-2 A^{2015}-A^{2014}\right) $ is, $ -175 $, $ 2014 $, $ 2016 $, $ -25 $

MARKS App · Accepted Answer

- 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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