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Question
If \[A = \left[ a_{ij} \right]\] is a 3 × 3 diagonal matrix such that a11 = 1, a22 = 2 a33 = 3, then find |A|.
Solution
\[I\text{ If }A = \left[ a_{ij} \right]\text{ is a diagonal matrix of order n, then }\left| A \right| = a_{11} \times a_{22} \times a_{33} \times . . . \times a_{nn} . \]
\[\text{ Given }: a_{11} = 1, a_{22} = 2\text{ and }a_{33} = 3\]
\[ \Rightarrow \left| A \right| = 1 \times 2 \times 3 = 6 \left[\text{ Applying the above property }\right]\]
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