Question

If A is a square matrix of order 3 × 3, then |KA| is equal to:
1. K² |A|
2. K |A|
3. 3K |A|
4. 9K|A|
5. K3 |A|

Answer 1

Correct Answer - Option 5 : K3 |A|

Concept:

Properties of determinants:​

• For a n×n matrix A, det(kA) = kⁿ det(A).

 

Calculation:

From the properties of the determinants, we know that |KA| = Kⁿ |A|, where n is the order of the determinant.

Here, n = 3, therefore, the answer is K³ |A|.