\[\left| \,\begin{matrix} {{({{a}^{x}}+{{a}^{-x}})}^{2}} & {{({{a}^{x}}-{{a}^{-x}})}^{2}} & 1 \\ {{({{b}^{x}}+{{b}^{-x}})}^{2}} & {{({{b}^{x}}-{{b}^{-x}})}^{2}} & 1 \\ {{({{c}^{x}}+{{c}^{-x}})}^{2}} & {{({{c}^{x}}-{{c}^{-x}})}^{2}} & 1 \\ \end{matrix}\, \right|=\][UPSEAT 2002; AMU 2005]

\[{{a}^{2}}{{b}^{2}}{{c}^{2}}\]

\[\left| \,\begin{matrix} {{({{a}^{x}}+{{a}^{-x}})}^{2}} & {{({{a

1.	\[\left\| \,\begin{matrix} {{({{a}^{x}}+{{a}^{-x}})}^{2}} & {{({{a}^{x}}-{{a}^{-x}})}^{2}} & 1 \\ {{({{b}^{x}}+{{b}^{-x}})}^{2}} & {{({{b}^{x}}-{{b}^{-x}})}^{2}} & 1 \\ {{({{c}^{x}}+{{c}^{-x}})}^{2}} & {{({{c}^{x}}-{{c}^{-x}})}^{2}} & 1 \\ \end{matrix}\, \right\|=\][UPSEAT 2002; AMU 2005]
A.	0
B.	\[2abc\]
C.	\[{{a}^{2}}{{b}^{2}}{{c}^{2}}\]
D.	None of these
Answer» B. \[2abc\]

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\[\left| \,\begin{matrix} {{({{a}^{x}}+{{a}^{-x}})}^{2}} & {{({{a}^{x}}-{{a}^{-x}})}^{2}} & 1 \\ {{({{b}^{x}}+{{b}^{-x}})}^{2}} & {{({{b}^{x}}-{{b}^{-x}})}^{2}} & 1 \\ {{({{c}^{x}}+{{c}^{-x}})}^{2}} & {{({{c}^{x}}-{{c}^{-x}})}^{2}} & 1 \\ \end{matrix}\, \right|=\][UPSEAT 2002; AMU 2005]

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