Question

If \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is a square root of identity matrix of order 2, then

• A. \(1+\alpha^2+\beta\gamma=0\)
• B. \(1+\alpha^2-\beta\gamma=0\)
• C. \(1-\alpha^2+\beta\gamma=0\)
• D. \(\alpha^2+\beta\gamma=1\)

Hint:

Matrix square roots satisfy \(A^2=I\).

Answer 1

The Correct Option is B

Step 1: Square the matrix and equate to identity matrix.
Step 2: Comparing elements gives: \[ 1+\alpha^2-\beta\gamma=0 \]