If $A$ is a square matrix of order $3$ such that $\det (A)=5$, then what is the value of $\det (3A)$?

Solution

1. Given that $A$ is a matrix of order $n=3$ and $\det (A)=5$.
2. The property of determinants states that $\det (kA)=k^n\det (A)$.
3. Substituting the values, we get $\det (3A)=3^3\times \det (A)$.
4. Calculating the value, $27\times 5=135$.
5. Hence the answer is (C).