GATE (TF) Textile 2009 Question Paper Solution | GATE/2009/TF/22

Question 22 (Textile Engineering & Fibre Science)

If the determinant and trace of a 2×2 matrix M are -1 and 0 respectively, then the determinant of M+M^{-1} is

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Option A is correct


Determinant of 2×2 matrix M is -1

As we know ,the determinant of the matrix=product of the eigen values

Let ,eigen values are a and b

So, -1=a x b


Trace of a 2×2 matrix M is 0

As we know, trace of the matix=sum of the eigen values




a x -a=-1


a=1 and b=-1

so, eigen values of matrix M are 1 & -1.

and eigen values of matrix M^-1 are 1 & -1

Eigen values of matrix M+M^-1 are (1+1) and (-1-1) i.e. 2 & -2
Determinant of M+M^-1=2\times -2=-4 (Ans)

Option A is correct.

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