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I have two matrices A and B,

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 have to proves theoretically that two of the eigenvalues of A and B are equal and remaining two eigenvalues of A are 1,1.

I tried it by calculating the determinant of A and B and I got close to the result but I am not able to prove it completely.

I got result like this,

sum of roots of determinant of A and B as

p+q+r+s=p1+q1 (p,q,r,s are roots of det of A, p1,q1 are roots of det of B)

Product of roots

p*q*r*s=p1*q1

pqr+qrs+prs+pqs=-2(p1*q1).

Please help me to show that two eigenvalues of A and B are equal.

Thanks.

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# Eigenvalues of two matrices are equal

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