We are given that,

Order of matrix = 3

|A| ≠ 0

|3A| = k|A|

We need to find the value of k.

In order to find k, we need to solve |3A|.

Using property of determinants,

|kA| = kⁿ|A|

Where, order of A is n × n.

Similarly,

|3A| = 3³|A|

[∵, order of A is 3]

⇒ |3A| = 27|A| …(i)

As, according to the question

|3A| = k|A|

Using (i),

⇒ 27|A| = k|A|

Comparing the left hand side and right hand side, we get

k = 27

Thus, the value of k is 27.