Instead of reasoning through sequences of rotations (e.g., Z followed by X), I found it clearer to directly construct the rotation matrix by mapping each axis. Since the columns of a rotation matrix specify the images of the x-, y-, and z-axes, we assign them directly: x maps to z, y to –x, and z to –y. The resulting matrix, equivalent to MakeXRotation composed with MakeZRotation, is

\(\begin{bmatrix} 0 & -1 & 0 \ 0 & 0 & -1 \ 1 & 0 & 0 \end{bmatrix}\)