Let \(A=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)\) be a \(2 \times 2\) real matrix with \(\operatorname{det} A=1\). If the equation \(\operatorname{det}\left(A-\lambda I_{2}\right)=0\) has imaginary roots \(\left(I_{2}\right.\) be the Identity matrix of order 2), then
(A) \((a+d)^{2}<4\)
(B) \((a+d)^{2}=4\)
(C) \((a+d)^{2}>4\)
(D) \((a+d)^{2}=16\)