Question

If for the matrix A = `[(α, -2),(-2, α)]`, |A³| = 125, then the value of α is ______.

Options

• ±3

• –3

• ±1

• 1

Answer 1

If for the matrix A = `[(α, -2),(-2, α)]`, |A³| = 125, then the value of α is ±3.

Explanation:

Given, `A = [(α, -2),(-2, α)]`

`\implies` |A| = α² – 4  ...(i)

Also, given |A³| = 125

`\implies` |A|³ = 125

`\implies` |A| = 5

`\implies` α² – 4 = 5   ...[From equation (i)]

`\implies` α² = 9

`\implies` α = ±3