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Let \( \mathrm{A}=\mathrm{a}_{\mathrm{ij}} \) be a matrix of order 3 where \( \mathrm{a}_{\mathrm{ij}}=\left[\begin{array}{ll}\mathrm{x} & \text { if } \quad \mathrm{i}=\mathrm{j}, \mathrm{x} \in \mathrm{R} \\ 1 & \text { if } \quad \mathrm{i}-\mathrm{j} \mid=1 \\ 0 & \text { otherwise }\end{array}\right. \), then which of the following hold(s) good?
(A) for \( x=2, A \) is a diagonal matrix.
(B) \( \mathrm{A} \) is a symmetric matrix
(C) for \( x=2 \), det \( A \) has the value equal to 6
(D) \( \operatorname{Let} \mathrm{f}(\mathrm{x})=\operatorname{det} \mathrm{A} \), then the function \( \mathrm{f}(\mathrm{x}) \) has both the maxima and minima.
\( \mathrm{P} \)
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