Question: Computing eigenvalues with assumptions

I am trying to simplify the eigenvalues of a 2x2 matrix [[a,b],[c,d]] subject to the condition a,b,c, and d are integers such that a+b = c+d. Why do the following commands not achieve this?



Eigenvalues(A) assuming a::integer,b::integer,c::integer,d::integer,a+b=d+c

How might I achieve what I need?

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