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GATE 2016 Set 2 Question No 6

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The question is quite simple but :

I wanted to confirm ,

What isthe Eigen values of the matrix  A are 1, 2, 4. Then What is the determinant of transpose matrix of "inverse of A"

1/8 is my answer
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Yup, the answer is  1/8.

Given that 1,2,4 are eigen values of A ⇒ |A| = 8 and

|inv(A)| = 1/|A| = 1/8

and Det(A)= Det(Tranpose A)

So, it will be 1/8 = 0.125
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