Question

If $A$ and $B$ are square matrices of order $3$ such that $|A|=-1,|B|=3$, then $|3AB|$ equals

• A. $-9$
• B. $-81$
• C. $-27$
• D. $81$

Answer 1

Answer: (B)

$-81$

We have $|kA|=k^{n}A$ where n is an order of the matrix.

and $|AB|=|A||B|$
So, $|3AB|=3^3|A||B|$

$\Rightarrow |3AB|=-81$