Question:
A matrix $A$ of order $3 \times 3$ has determinant 5 . What is the value of $|3 A| ?$
Solution:
If $A=\left[a_{i j}\right]$ is a square matrix of order $n$ and $k$ is a constant, then
$|\mathrm{kA}|=\mathrm{k}^{\mathrm{n}}|\mathrm{A}|$
Here,
Number of rows $=n$
$k$ is a common factor from each row of $k$
$|3 \mathrm{~A}|=3^{3}|\mathrm{~A}|=27 \times 5=135$
[Given matrix is $3 \times 3$ such that $|\mathrm{A}|=5$ ]
Thus, $|3 \mathrm{~A}|=135$