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Question: Answered & Verified by Expert
Let \( A \) be a square matrix of order \( 3 \times 3 \), then \( |5 A|= \)
MathematicsDeterminantsKCETKCET 2018
Options:
  • A \( 5|A| \)
  • B \( 125|A| \)
  • C \( 25|\mathrm{~A}| \)
  • D \( 15|A| \)
Solution:
1904 Upvotes Verified Answer
The correct answer is: \( 125|A| \)
We know that, for \( n \times n \) matrix \( |k A|=k^{n}|A| \).
So, for \( 3 \times 3 \) matrix is
\( |5 A|=5^{3}|A|=125|A| \)

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