If the matrix A=[\table \alpha , \beta ; \beta , \alpha] is such that A^2=1, then which one of the following is correct?

Correct Answer is : α=0,β=1 or α=1,β=0

\alpha=0, \beta=1 or \alpha=1, \beta=0

\alpha=0, \beta \neq 1 or \alpha \neq 0, \beta=1

\alpha=1, \beta \neq 0 or \alpha \neq 1, \beta=0

UPSC NDA I 2011 Mathematics Paper

Question : 84 of 120

Marks: +1, -0

If the matrix A=[

α	β
β	α

] is such that A2=1, then which one of the following is correct?

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α2+β2	2αβ
2αβ	β2+α2

−α	β
−β	α