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Question

If A=[4131] then the determinate of the matrix A20162A2015A2014 is

A
2014
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B
2016
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C
175
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D
25
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Solution

The correct option is B 25
Given that
A=[4131]
|A20162A2015A2014|=?
|A2014||A22AI|
=|A|2014[A22AI]
A2=A.A=[4131][4131]
A2=[1634112+33+1]=[13392]
So,
|A|2014[[13392]2[4131][1001]]
=|A|2014[[13392][8262][1001]]
=|A|2014[13+813+20960221]
=|A|2014[205155]
|A|=[4131]=4×1(1)×3
=4+3=1
then
|A|2014[205155]
(1)2014[100+75]
(1)2014×(25)=1×(25)
=25
Hence this is though

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