If A = pmatrix x & y & z y & z & x z & x & y pmatrix where x , y ,...

Given the matrix $A = \begin{pmatrix} x & y & z \\ y & z & x \\ z & x & y \end{pmatrix}$.

The transpose of $A$ is given by:

$A^T = \begin{pmatrix} x & y & z \\ y & z & x \\ z & x & y \end{pmatrix}$

We can observe that $A^T = A$, which means $A$ is a symmetric matrix.

It is given that $A$ is an orthogonal matrix. By the definition of an orthogonal matrix, we have:

$A A^T = I$

Substituting $A^T = A$ into the above equation, we get:

$A A = I$

$A^2 = I$

Thus, $A^2$ is equal to the identity matrix.

Answer: Identity matrix