Eigenvalues of 2 matrices are equal

[gopi9]

Hi all,

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

 

[AlephZero]

We've already had one attempt at this.
https://www.physicsforums.com/showthread.php?p=4507869#post4507869