A,B are n*n matrices over C.
give a counterexample satisfies trace(A)=trace(B), det(A)=det(B)
but their eigenvalues are not the same.
trace(A)=x and det(A)=y
This gives you two equations in the diagonal elements (the eigen values) of A. Now assume A is a 3x3 matrix and show that the two equations have multiple solutions (and find two or more of them for some convienient choice of x and y).