If \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) are such that \( \mathrm{A}+\mathrm{B}+\mat....

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If \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) are such that \( \mathrm{A}+\mathrm{B}+\mathrm{C}=0 \), then the value of \( \left|\begin{array}{ccc}1 & \cos \mathrm{C} & \cos \mathrm{B} \\ \cos \mathrm{C} & 1 & \cos \mathrm{A} \\ \cos \mathrm{B} & \cos \mathrm{A} & 1\end{array}\right| \) is
P
(A) 1
(B) \( 1-\cos ^{2} \mathrm{~A}-\cos ^{2} \mathrm{~B}-\cos ^{2} \mathrm{C}-2 \cos \mathrm{A} \cos \mathrm{B} \cos \mathrm{C} \)
(C) 0
(D) -1


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