Question

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

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

Answer 1

The correct option is B $-81$

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

$|3AB|=3^3|AB|=27|A||B|=-81$

[Since $|AB|=|A|.|B|$ and $|aA|=a^3|A|$ for $A$ being $3\times 3$ matrix and $a\ne 0$ is scalar.]