matrix adjoint

Question

If $1,-2,3$ are the eigen values of the matrix $A$ then ratio of determinant of $B$ to the trace of $B$ is_______where $B=[adj(A)-A-A^{-1}-A^{2}]$

Comments

is it -3:2?

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this is the answer 

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Apply, $AdjA = \frac{|A|}{A}$ and $A^{-1} = \frac{1}{A}$

Then for each value of $A$ you will get $B = -7, \frac{1}{2}, \frac{-41}{3}$

Computing Determinanat = 47.6

Computing Trace = -20.17

Hence by dividing you will get = -2.3

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@ashwin can you please elaborate how you are calculating B,it would be of great help to me...little dense in linear algebra :p

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@aditya

pls check this

https://math.stackexchange.com/questions/100161/eigenvalues-of-adjoint-of-non-singular-matrix

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B=[ adjA - A + A^-1 - A^2] if  i put plus sign before the inverse term, i get the right answer. But the question is not that!

* I tried with negative sign and get the wrong answer.  Please explain?.

Answer 1

Please rotate it :p