Question

If \( A = \begin{bmatrix} a & b \\ b & a \end{bmatrix} \) and \( (AI)^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix} \), where \( I \) is the identity matrix, then __________.

• A. \( \alpha = a^2 + b^2,\; \beta = 2ab \)
• B. \( \alpha = 2ab,\; \beta = a^2 + b^2 \)
• C. \( \alpha = a^2 + b^2,\; \beta = ab \)
• D. \( \alpha = a^2 + b^2,\; \beta = a^2 - b^2 \)

Hint:

Identity matrix does not change a matrix: \( AI = A \). Always simplify before squaring.

Answer 1

The Correct Option is A