Question

If $A$ is a $3\times 3$ matrix $\left|3A\right|=k\left|A\right|$, then write the value of $k.$

Answer 1

If $A$ is $n\times n$ matrix then for any integer $p$ , $|pA|=p^n|A|$
Since here $A$ is $3\times 3$ matrix , we get $|3A|=3^3|A|$ which is equal to $k|A|$ (given).Therefore $k=3^3=27$.