Question

If A is a square matrix of order 3 such that |A| = 4 then find the value of |3A| ?
1. 27
2. 108
3. 81
4. None of these

Answer 1

Correct Answer - Option 2 : 108

CONCEPT:

• If A is a matrix of order n, then |k ⋅ A| = kⁿ ⋅ |A|, where k ∈ R.

CALCULATION:

Given: A is a square matrix of order 3 such that |A| = 4

Here, we have of find the value of |3A|

As we know that, if A is a matrix of order n, then |k ⋅ A| = kn ⋅ |A|, where k ∈ R.

⇒ |3A| = 3³ × 4 = 108

Hence, the correct option is 2.