Geometric Solution : See A as a transformation matrix.
When the image of every circle is a circle of same radius, it means that there is no scaling or change in orientation of axes. This occurs when A is a rotation matrix A = $\begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ which is an orthogonal matrix.
So $(A)$ is correct