If A and B are square matrices of order 3 such that \(|A|= 3\) and \(|B|=-1\), then \(|3AB|\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −81
Two standard properties are used: \(|kM| = k^n|M|\) for a square matrix M of order n, and \(|AB| = |A||B|\).
AB is of order 3, so
\(|3AB| = 3^3|AB|\)
\(= 27|A||B|\)
\(= 27 \times 3 \times (-1) = -81\)
Tip: A scalar multiplies every row, so \(|kM| = k^n|M|\), not \(k|M|\). Taking \(|3AB| = 3|AB|\) gives −9, Option (1).