If for the matrix, A = 1 - α α β , A A T = I 2 , then the value of α 4 + β 4 is :

Step-by-step solution

A = 1 - α α β    A A T = I 2 ⇒ 1 - α α β 1 α - α β = 1 0 0 1 ⇒ 1 + α 2 α - α β α - α β α 2 + β 2 = 1 0 0 1 ⇒ 1 + α 2 = 1   &   α 2 + β 2 = 1 ⇒ α 2 = 0   &   β 2 = 1 ∴   α 4 = 0   &   β 4 = 1 ∴   α 4 + β 4 = 1