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JEE Math Practice Question

If for the matrix, $$A = \left[ {\begin{matrix} 1 & { - \alpha } \\ \alpha & \beta \\ \end{matrix} } \right]$$, $$A{A^T} = {I_2}$$, then the value of $${\alpha ^4} + {\beta ^4}$$ is :

  1. A.3
  2. B.2
  3. C.1
  4. D.4

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