If A and B are square matrices of order 3 such that $|A|= 3$ and $|B|=-1$, then $|3AB|$ is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -81
Given
$|A|=3,\;|B|=-1$
Order of matrices is $3\times3$.
Use property:
$|kA|=k^{n}|A|$ for an $n\times n$ matrix.
So
$|3AB|=3^{3}|AB|$
Also
$|AB|=|A||B|$
Thus
$|3AB|=27\cdot3\cdot(-1)$
$=-81$