If \( A \) and \( B \) are square matrices of order 3 × 3 such that \( |A|=7 \) and \( |B|=6 \), then \( |B\,\mathrm{adj}\,A|= \)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 294
For a matrix of order n, \( |\mathrm{adj}\,A|=|A|^{n-1} \), and for any two such matrices \( |XY|=|X|\,|Y| \). Here n = 3:
\( \displaystyle |\mathrm{adj}\,A|=|A|^{2}=49 \)
\( \displaystyle |B\,\mathrm{adj}\,A|=|B|\,|\mathrm{adj}\,A| \)
\( \displaystyle =6\times 49=294 \)
Why the other options are incorrect
Option (1) 42 — Incorrect. 42 = |B| × |A|; adj A has been treated as A, but \( |\mathrm{adj}\,A|=|A|^2 \).
Option (2) 942 — Incorrect. The value is \( 6\times 49=294 \), not 942.
Option (3) 284 — Incorrect. The value is \( 6\times 49=294 \), not 284.