GATE 2008 C.E.

Question

The eigen values of the matrix [P] = |4     5| are?

                                                                |2    -5|
The answer for this is -6 and 5.

My question is what wrong am I doing by R1 = R1 + R2 and converting it to lower triangular matrix. Answer after this is +6 and -5 i.e. sign of eigen values inverted.

Comments

Elementary operations on matrix changes the eigen values of the matrix (although the determinant remains the same).

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Isn't this wrong then -> https://gateoverflow.in/117446/gate-ece-2017-eigen-value

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One of the comments in the link mentions that if the sum of all columns or rows are same,then that sum is equal to one of the eigen values(I'm not sure about this property).However,even if we assume the property to be true,in this case neither the sum of all the rows nor the sum of all columns are the same,so we cannot apply elementary operations to find the eigen values.Link to the answer to that question - https://www.youtube.com/watch?v=-R9xV89BXL4.