Consider the matrix [A=left(begin{array}{ccc} frac{1}{2} & frac{1}{sqrt{2}} & frac{1}{2} -frac{1}{sqrt{2}} & 0 & frac{1}{sqrt{2}} frac{1}{2} & -frac{1}{sqrt{2}} & frac{1}{2} end{array} ight)] a. Verify

Consider the matrix

\[A=\left(\begin{array}{ccc} \frac{1}{2} & \frac{1}{\sqrt{2}} & \frac{1}{2} \\ -\frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ \frac{1}{2} & -\frac{1}{\sqrt{2}} & \frac{1}{2} \end{array}\right)\]

a. Verify that this is a rotation matrix.

b. Find the angle and axis of rotation.

c. Determine the corresponding similarity transformation using the results from part \(b\).