# Show that the matrix represents a series of rotation and reflection

Problem: Show that the matrix $$A=\begin{bmatrix} 0 & -1 & 0\\ 1 & 0 & 0\\ 0 & 0 & -1 \end{bmatrix}$$ represents a rotation $$R_\theta$$ about a line $$l$$ through the origin followed by a reflection $$H_l$$ about the plane through the origin that is perpendicular to the line $$l$$. You have to find the standard matrices of $$R_\theta$$ and $$H_l$$.

My Attempt: I calculated the determinant of A which was -1. I know that A is a orthogonal matrix, and since it has a determinant of -1, it involves reflection. However, I can't think of a way to find the line $$l$$.
Hint: $$A$$ looks a lot like the rotation matrix $$R_{\theta} = \pmatrix{0&-1&0\\1&0&0\\0&0&1}.$$