For example, try [x1 x2 x3] = [1 0 0]; => [x2 x3 x1] = [0 0 1]. i.e the x and z axes. The axis of rotation is the y-axis and the angle is pi/2. (From the dot product)
For the next rotation in the cycle, z axis to y axis, the axis of rotation is the x-axis and the angle is pi/2 again. Then...
You can answer this problem, knowing anything about vectors or matrices. Just look at what you are given and think about what it means.
Any point on the axis of rotation doesn't move when it is rotated. If [x1 x2 x3] rotates to [x2 x3 x1], then any point [a a a] is rotated to [a a a].
Since...