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

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a

2014

b

2016

c

-175

d

-25

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detailed solution

Correct option is B

Let B=A2016−2A2015−A2014 Then ,B=A2014A2−2A−I⇒ |B|=|A|2014A2−2A−INow, A−−4 −13 1∴A2−2A−I=−4−131−4−131−2−4−131−1001=133−9−2+82−6−2+−100−1=205−15−5⇒ A2−2A−I=205−15−5=−25and |A|=−4 −13 1=−1 Hence, |B|=(−1)2014=−25

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