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प्रश्न
If A = [aij] is a 3 × 3 scalar matrix such that a11 = 2, then write the value of |A|.
उत्तर
A scalar matrix is a diagonal matrix, in which all the diagonal elements are equal to a given scalar number.
\[\text{ Given: }A = \left[ a_{i j} \right]\text{ is 3} \times\text{ 3 matrix, where }a_{11} = 2 \]
\[ \Rightarrow A = \begin{bmatrix} 2 & 0 & 0\\0 & 2 & 0\\0 & 0 & 2 \end{bmatrix} \]
\[ \Rightarrow \left| A \right| = \begin{vmatrix} 2 & 0 & 0\\0 & 2 & 0\\ 0 & 0 & 2 \end{vmatrix}\]
\[ = 2 \times \begin{vmatrix} 2 & 0\\ 0 & 2 \end{vmatrix} \left[\text{ Expanding along }C_1 \right]\]
\[ = 2 \times 2 \times 2 = 8\]
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