Question

Choose the correct alternative.

If A = `[(α, 4),(4, α)]` and |A³| = 729, then α = ______.

Options

• ±3

• ±4

• ±5

• ±6

Answer 1

If A = `[(α, 4),(4, α)]` and |A³| = 729, then α = ±5.

Explanation:

|A| = `[(α, 4),(4, α)]` = α² – 16

|A|³ = 729 = 9³ 

∴ |A| = 9

∴ α² – 16 = 9

∴ α² = 25

∴ α = ±5.