If A = [[α, β], [γ, −α]] is such that A² = I, then which of the following relations is true?

If A = [[α, β], [γ, −α]] is such that A² = I, then which of the following relations is true?

• A. 1 + α² + βγ = 0
• B. 1 − α² + βγ = 0
• C. 1 − α² − βγ = 0
• D. 1 + α² − βγ = 0

Answer: C) 1 − α² − βγ = 0

Explanation: A² = [[α, β], [γ, −α]] × [[α, β], [γ, −α]] = [[α² + βγ, 0], [0, βγ + α²]]. Equating to I gives α² + βγ = 1, which rearranges to 1 − α² − βγ = 0.