If A^{2}+B^{2}+C^{2}=0, then what is the value of the following? \begin{vmatrix}1&\cos C&\cos B\\ \cos C&1&\cos A\\ \cos B&\cos A&1\end{vmatrix}

Explanation

Since A^2+B^2+C^2=0 for real values, A=B=C=0. Then \cos A = \cos B = \cos C = 1. The determinant has all elements as 1, so its value is 0.

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