For a square matrix \( A \) of order 3, if \( |A|=-3 \), then \( |4\,\mathrm{adj}\,A| \) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 576
For a square matrix of order n, \( |k\mathrm{B}|=k^n|\mathrm{B}| \) and \( |\mathrm{adj\,A}|=|\mathrm{A}|^{n-1} \). Here n = 3.
\( \displaystyle |\mathrm{adj\,A}|=(-3)^{3-1}=9 \)
\( \displaystyle |4\,\mathrm{adj\,A}|=4^3\times|\mathrm{adj\,A}| \)
\( \displaystyle =64\times 9=576 \)