Question

If A = `[(a, b),(b, a)]` and A² = `[(α, β),(β, α)]`, then ______.

Options

• α = 2ab, β = a² + b²

• α = a² + b², β = ab

• α = a² + b², β = 2ab

• α = a² + b², β = a² – b²

Answer 1

If A = `[(a, b),(b, a)]` and A² = `[(α, β),(β, α)]`, then `underlinebb(α = a^2 + b^2, β = 2ab)`.

Explanation:

A² = `[(α, β),(β, α)]`

`\implies` A.A = `[(a, b),(b, a)][(a, b),(b, a)]`

= `[(a^2 + b^2, 2ab),(2ab, a^2 + b^2)]`

α = a² + b²; β = 2ab