If A and B are square matrices of order 3 such that $|A|= -1$ and $|B|= 5$, then the value of $|3AB|$ is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → -135
Given:
$|A| = -1$, $|B| = 5$, order of $A$ and $B$ is $3 \times 3$.
Property: For an $n \times n$ matrix, $|kM| = k^n |M|$ and $|AB| = |A|\,|B|$.
$|3AB| = 3^3 \, |AB|$
$= 27 \cdot (|A| \cdot |B|)$
$= 27 \cdot (-1) \cdot 5$
$= -135$