If \( A \) is a square matrix of order 3 and |A| = 6, then the value of \( |2A^T| \) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 48
Two results are needed: \( |kA|=k^n|A| \) for a matrix of order n, and \( |A^T|=|A| \).
\( \displaystyle |2A^T|=2^3|A^T| \)
\( \displaystyle =8|A| \)
\( \displaystyle =8\times 6=48 \)
Why the other options are incorrect
Option (1) 40 — Incorrect. 40 is not a multiple of 6, while \( |2A^T| \) must be \( 2^3\times 6 \).
Option (3) 12 — Incorrect. 12 = 2 × 6 takes the factor 2 out only once; it comes out once from each of the 3 rows.
Option (4) 24 — Incorrect. 24 = 22 × 6 uses the power 2 instead of the order 3.