A) \[1+{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]
B) \[1-{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\]
C) \[1+{{a}^{2}}+{{b}^{2}}-{{c}^{2}}\]
D) \[1+{{a}^{2}}-{{b}^{2}}+{{c}^{2}}\]
Correct Answer: A
Solution :
\[\left| \,\begin{matrix} 1 & a & b \\ -a & 1 & c \\ -b & -c & 1 \\ \end{matrix}\, \right|=1\,(1+{{c}^{2}})-a(-a+bc)+b(ac+b)\] = \[1+{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\].
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