If \( A \) is a \( 3\times 3 \) matrix with \( |A|=4 \), then \( |4A| \) is equal to :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 256
For a square matrix of order n, \( |kA|=k^n|A| \). Here n = 3.
\( \displaystyle |4A|=4^3\times|A| \)
\( \displaystyle =64\times 4 \)
\( \displaystyle =256 \)
Why the other options are incorrect
Option (1) 16 — Incorrect. This multiplies |A| by 4 only once, as if |4A| were 4|A|.
Option (3) 64 — Incorrect. This is only \( 4^3 \); it leaves out the factor |A| = 4.
Option (4) 12 — Incorrect. The value is 256, not 12.