Choose the correct answer in the following questions: If A = [ α γ β − α ] is such that A 2 = I , then (a) 1 + α 2 + β γ = 0 (b) 1 − α 2 + β γ = 0 (c) 1 − α 2 − β γ = 0 (d) 1 + α 2 − β γ = 0

Question

Choose the correct answer in the following questions: If A = [ α γ ​ β − α ​ ] is such that A 2 = I , then (a) 1 + α 2 + β γ = 0 (b) 1 − α 2 + β γ = 0 (c) 1 − α 2 − β γ = 0 (d) 1 + α 2 − β γ = 0,

MARKS App · Accepted Answer

$ ​ A 2 = [ α γ ​ β − α ​ ] [ α γ ​ β − α ​ ] = [ α 2 + β γ α γ − α γ ​ α β − α β β γ + α 2 ​ ] = [ 1 0 ​ 0 1 ​ ] ​ 	herefore \mathrm{A}^2=\mathrm{I} \quad \alpha^2+\beta \gamma=1 \quad or \quad 1-\alpha^2-\beta \gamma=0$ Option (c) is correct.

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