Question

If $A$ is a $3\times 3$ matrix and $\text{det}\left(3A\right)=k\left(\text{det}A\right)$, then $k=$

• A. $9$
• B. $6$
• C. $1$
• D. $27$

Answer 1

The correct option is D $27$

The non zero determinant of a scalar multiple of a n×n matrix is given by the following property.

$|kA|=kn|A|$

⟹$|3A|=3^3|A|=27|A|$

$k=27$