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Question

Let A=[aij]4×4 be a matrix such that aij={2,if i=j0,if ij.
Then the value of {det(adj(adj A))7} is
( {.} represents the fractional part function )


A
17
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B
27
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C
37
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D
67
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Solution

The correct option is A 17
A is a scalar matrix, therefore |A|=24
We know that for a n×n matrix A,
|adj A|=|A|n1
|adj(adj A)|=|adj A|n1=|A|(n1)2
|adj(adj A)|=|A|(41)2=(24)9=236
{det(adj(adj A))7}={2367}
={(7+1)127}
={ 12C0712+12C1711+12C2710++12C1171+12C12707}
={7k+17}; kN
=17

Mathematics

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