A and B are square matrices of order 3 each such that \( |A|=3,|B|=2 \), then the value of \( |4AB| \) will be?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 384
For square matrices of order n, \( |kM|=k^{n}|M| \) and \( |AB|=|A|\,|B| \). Here n = 3:
\( |4AB|=4^{3}\,|AB| \)
\( =64\,|A|\,|B| \)
\( =64\times 3\times 2=384 \)
Tip: A scalar comes out of a determinant of order n as \( k^{n} \), not k: taking out only 4 would give 24.