If `A=[[alpha,beta],[gamma,alpha]]`is such that `A^2=I`, then (A) `1+alpha^2+betagamma=0` (B) `1-alpha^2+betagamma=0` (C) `1-alpha^2-betagamma=0` (D) `1+alpha^2-betagamma=0`

Explanation

To solve the problem, we start with the matrix \( A \) defined as:

\[ A = \begin{pmatrix} \alpha & \beta \\ \gamma & \alpha \end{pmatrix} \]

We are given that \( A^2 = I \), where \( I \) is the identity matrix:

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