Sequence of rotation matrices I want a rotation matrix $R$ that transforms +x axis to +y, +y to +z, and +z to +x. One way of doing it is by a rotation about +x by 90 deg anti-clockwise, followed by a rotation about +y by 90 deg anti-clockwise. The matrices respectively are:
$$R_1 = \begin{bmatrix}
1 & 0 & 0 \\
0 & 0 & -1 \\
0 & 1 & 0 \\
\end{bmatrix}$$
$$R_2 = \begin{bmatrix}
0 & 0 & 1 \\
0 & 1 & 0 \\
-1 & 0 & 0 \\
\end{bmatrix}$$
Since R1 first operates first followed by R2, the resultant, I think, is R=(R2)(R1). But when I cross-check by applying R to an arbitrary point, say (1,2,3), I don't get the right transform of (3,1,2). Instead, I get it right when I do R=(R1)(R2)  which doesn't make sense to me. Please help

The matrix
$$
            M = \left[\begin{array}{ccc}0 & 0 & 1 \\
                                        1 & 0 & 0 \\
                                        0 & 1 & 0 \end{array}\right]
$$
maps $+x$ to $+y$, maps $+y$ to $+z$ and $+z$ to $+x$. You can see this by direct verification. Because it maps a right-hand triple to a right-hand triple, then $M$ is a rotation matrix. (You can also see that $\mbox{det}(M)=1$.)
