QJEEM21Mab8f7: JEE Main 2021 Mathematics - Class 12 JEEM21Mab8f7 Solution: If for the matrix, A = [ 1 − α α β ] , , then the value of is :

Question

Verified Solution • 2025–26 Session moderate

If for the matrix,

A = [\begin{matrix} 1 & - α \\ α & β \end{matrix}]

,

A{A^T} = {I_2}

, then the value of

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

is :

Accepted Answer

[\begin{matrix} 1 & - α \\ α & β \end{matrix}] [\begin{matrix} 1 & α \\ - α & β \end{matrix}] = [\begin{matrix} 1 + α^{2} & α - α β \\ α - α β & α^{2} + β^{2} \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]

1 +

\alpha

² = 1

\alpha

² = 0

\alpha

² +

\beta

² = 1

\beta

² = 1

\alpha

⁴ = 0

\beta

⁴ = 1

\alpha

⁴ +

\beta

⁴ = 1

Step-by-Step Verified Solution