Question

Given that A is a non-singular matrix of order 3 such that A² = 2A, then the value of |2A| is:

Options

• 4

• 8

• 64

• 16

Answer 1

64

Explanation:

A² = 2A

|A²| = |2A|

|A|² = 2³ |A| as |kA| = kⁿ |A| for a square matric of order n

either |A| = 0 or |A| = 8

But A is non-singular matrix

∴ |A| = 8² = 64