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Question

If A=[−4−131], then the determinant of the matrix (A2016−2A2015−A2014) is

A
2014
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B
175
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C
2016
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D
25
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Solution

The correct option is D 25
|A20162A2015A2014|
=|A|2014|A22AI|
Now, |A|=4+3=1
and A22AI=[205155]
|A22AI|=25
|A20162A2015A2014|
=(1)2014×(25)=25

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