If \(A\) and \(B\) square matrices of order 3 such that \(|A| = -1, |B| = 5\), then the value of \(|2AB|\) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → −40
For a square matrix of order n, \(|kA| = k^n|A|\); also \(|AB| = |A||B|\). Here n = 3:
\( |2AB| = 2^3|AB| = 8|A||B| \)
\( = 8 \times (-1) \times 5 = -40 \)
Why the other options are incorrect
Option (2) −10 — Incorrect. This is \(2|A||B|\). The factor 2 multiplies each of the 3 rows, so it comes out as \(2^3\).
Option (3) 20 — Incorrect. \(|A||B| = -5\) is negative and \(2^3 \gt 0\), so \(|2AB|\) is negative.
Option (4) −20 — Incorrect. This is \(2^2|A||B|\); the power of 2 must be the order, 3.