A matrix A of order 3 × 3 has determinant 5.

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, $|3 \mathrm{~A}|=135$