If \(A\) is a square matrix of order 3 and \(|A| = -5\), then \(|3A|\) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → −135
For a square matrix of order n, \(|kA| = k^n|A|\), because each of the n rows is multiplied by k. Here n = 3:
\(|3A| = 3^3 \times (-5)\)
\(|3A| = 27 \times (-5) = -135\)
Tip: \(|kA| = k^n|A|\), not k|A|: writing 3 × (−5) = −15 is a common slip.