If for the matrix, A=[\table 1 , -\alpha ; \alpha , \beta], A A^{T}=I_{2}, then the value of \alpha^{4}+\beta^{4} is [25 Feb 2021 Shift 2]

JEE Main 25 Feb 2021 Shift 2 Solved Paper

Section: Mathematics

Question : 61 of 90

Marks: +1, -0

If for the matrix, A=[

1	−α
α	β

],AAT=I2, then the value of α4+β4 is

[25 Feb 2021 Shift 2]

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1+α2	α−αβ
α−αβ	α2+β2