A (2 xx 2) matrix [[a,c+id],[c-id,b]] where a, b, c, d are real constants will have two different eigenvalues unless it is a multiple of the identity matrix. i used this |A-lambda I|=det(A-lambda I)=0 to prove that it will have 2 eigenvalues. How do i prove that it will only have 1 when it is a multiple of the identity matrix?

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