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If A = [a b; b a] and A² = [α β; β α], then

1. α = 2ab, β = a² + b²
2. α = a² + b², β = ab
3. α = a² + b², β = 2ab
4. α = a² + b², β = a² - b²

Correct answer: α = a² + b², β = 2ab

Solution

The correct option states that α equals the sum of the squares of the elements on the diagonal of matrix A, while β represents twice the product of the off-diagonal elements. This is derived from the matrix multiplication of A with itself, which results in the specified forms for α and β.

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