Let A be a square matrix of order 3 and I is an identity matrix of orders 3. If \( |A|=3 \), the value of \( |A(4I)| \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 192
Since \( A(4I)=4A \) and A is of order 3, \( |kA|=k^3|A| \):
\( \displaystyle |4A|=4^3|A| \)
\( \displaystyle =64\times 3 \)
\( \displaystyle =192 \)
Why the other options are incorrect
Option (1) 64 — Incorrect. This is only \( 4^3 \); it leaves out the factor |A| = 3.
Option (2) 3 — Incorrect. This is |A| alone; it leaves out the factor \( 4^3 \) from 4I.
Option (4) 12 — Incorrect. This multiplies |A| by 4 only once. For a 3 × 3 matrix, a factor 4 comes out of each of the three rows.