A is a square matrix of order 3 such that |A| = 13. The value of |−3A| is _____________.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −351
Multiplying a matrix by k multiplies every row by k, and each row gives one factor k in the determinant. For a square matrix of order n:
\(|kA| = k^n\,|A|\)
Here k = −3 and n = 3:
\(|-3A| = (-3)^3 \times 13\)
\(= -27 \times 13\)
\(= -351\)
Why the other options are incorrect
Option (1) −39 — Incorrect. This is −3 × 13: the factor −3 is taken only once, but it comes from each of the 3 rows.
Option (3) 117 — Incorrect. This is \((-3)^2 \times 13\), the rule for a matrix of order 2, not 3.
Option (4) 169 — Incorrect. This is \(13^2\); it does not contain the factor \((-3)^3\) at all.