If for the matrix, A = [ 1 - α α β ], A A^(T) = I₂, then the value of α ⁴ + β ⁴ is:

Matrices and Determinants: JEE Main 2021 Mathematics question

JEE Main 2021 · 25 Feb, Evening shift · Q4663

JEE Main 202125 Feb, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

If for the matrix,

A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]

A{A^T} = {I_2}

, then the value of

{\alpha ^4} + {\beta ^4}

is :

JEE Main 2021 · 25 Feb, Evening shift · Q4663

JEE Main 202125 Feb, Evening shiftMathematicsMediumMatrices and Determinants245× since 2002

If for the matrix,

A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]

A{A^T} = {I_2}

, then the value of

{\alpha ^4} + {\beta ^4}

is :