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Question

Let A=[aij] be a 4×4 matrix. If aij={2, when i=j0, when ij,
then the value of {det(adj(adjA))7} is
(where {.} represents the fractional part function)
  1. 17
  2. 37
  3. 27
  4. 47


Solution

The correct option is A 17
A=⎢ ⎢ ⎢2000020000200002⎥ ⎥ ⎥

|A|=24
We know that for a n×n matrix,
|adj A|=|A|n1
|adj A|=|A|3=212
|adj(adj A)|=|adj A|3=236

Now, {det(adj(adj A))7}
={2367}
={(7+1)127}=17

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