If A and B are square matrices of order 3 such that \(|A| = -1\) and \(|B| = 5\), then the value of \(|3AB|\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → −135
For a square matrix M of order n, \(|kM| = k^n|M|\), and \(|AB| = |A||B|\). Here n = 3:
\(|3AB| = 3^3|AB| = 27|A||B|\)
\(= 27 \times (-1) \times 5 = -135\)
Tip: \(|kM| = k^n|M|\), not k|M|: every one of the n rows is multiplied by k. Taking \(3|A||B|\) gives −15, Option (1).