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I have two matrices

A=0 0 1 0

0 0 0 1

a b a b

c d c d

and B=0 0 0 0

0 0 0 0

0 0 a b

0 0 c d

I need to prove that two eigenvalues of A and two eigenvalues of B are equal. I tried to take the determinant of A-λI and B-λI and solve them but the result is not complete, the result that I got is

if e,f,g,h are eigenvalues of A and i,j,k,l are eigenvalues of B then

e+f+g+h=a+d;

i+j=a+d, k=l=0;

e*f*g*h=i*j;

efg+fgh+efh+egh=-2ij

Can anyone get me the complete result that is two eigenvalues of A and B are equal?

Thanks

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# Eigenvalues of 2 matrices are equal

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