Q.

If  A=−4    −13  1 then the determinant line matrix A2016−2A2015−A2014, is

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a

2014

b

2016

c

-175

d

-25

answer is B.

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Detailed Solution

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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