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If A is a 2 × 2 matrix and |A| = 5, what is |5A| ? (| | denotes determinant)

If A is a 2 × 2 matrix and |A| = 5, what is |5A| ? (| | denotes determinant) Correct Answer 125

Concept:

Properties of determinants:​

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

Calculation:

Given:

|A| = 5

k = 5

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

Here, n = 2, therefore, the answer is K2 |A|.

|5A| = 52|A|

|5A| = 52 × 5 = 125

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