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Question
A matrix A of order 3 × 3 has determinant 5. What is the value of |3A|?
Solution
\[\text{ If }A = \left[ a_{i j} \right]\text{ is a square matrix of order n and k is a constant, then}\]
\[\left| kA \right| = k^n \left| A \right| \]
Here,
Number of rows = n
k is a common factor from each row of k
\[\left| 3A \right| = 3^3 \left| A \right| = 27 \times 5 = 135 \left[\text{ Given matrix is 3 }\times\text{ 3 such that }\left| A \right| = 5 \right]\]
\[\text{ Thus,} \left| 3A \right| = 135\]
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