If A is a square matrix of order 2 such that \(|A| = -5\), then the value of \(|-3A|\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(-45\)
Multiplying a matrix by k multiplies every row by k, and each row brings out one factor k. So for a matrix of order n:
\( |kA| = k^{n}|A| \)
Here n = 2 and k = −3:
\( |-3A| = (-3)^{2} \times (-5) \)
\( = 9 \times (-5) = -45 \)
Why the other options are incorrect
Option (1) 15 — Incorrect. This is \((-3) \times (-5)\); the factor −3 must be taken once for each of the 2 rows.
Option (2) 135 — Incorrect. This is \((-3)^{3} \times (-5)\), the value for a matrix of order 3.
Option (4) 45 — Incorrect. \((-3)^{2} = 9\) is positive, so the sign of \(|A| = -5\) stays; the result is negative.