Editing Rotation matrix (section)

=== Direction ===
The direction of vector rotation is counterclockwise if {{mvar|θ}} is positive (e.g. 90°), and clockwise if {{mvar|θ}} is negative (e.g. −90°) for <math>
  R(\theta)</math>. Thus the clockwise rotation matrix is found as (by replacing {{mvar|θ}} with {{mvar|-θ}} and using the trigonometric symmetry of <math display="inline">\sin(-\theta) = - \sin(\theta)</math> and <math display="inline">\cos( - \theta) = \cos(\theta)</math>)
:<math>
  R(-\theta) = \begin{bmatrix}
     \cos\theta & \sin\theta \\
     -\sin\theta & \cos\theta \\
  \end{bmatrix}.</math>

An alternative convention uses rotating axes (instead of rotating a vector),<ref>{{cite book |last=Swokowski |first=Earl |url=https://archive.org/details/studentsupplemen00bron |title=Calculus with Analytic Geometry |publisher=Prindle, Weber, and Schmidt |year=1979 |isbn=0-87150-268-2 |edition=Second |location=Boston |url-access=registration}}</ref> and the above matrices also represent a rotation of the ''axes clockwise'' through an angle {{mvar|θ}}.

The two-dimensional case is the only non-trivial case where the rotation matrices group is commutative; it does not matter in which order rotations are multiply performed. For the 3-dimensional case, for example, a different order of multiple rotations gives a different result. (E.g., rotating a cell phone along ''z''-axis then ''y''-axis is not equal to rotations along the ''y''-axis then ''z''-axis.)