Rotations, denoted by R, where c is a point in the plane (the centre of rotation), and θ is the angle of rotation. In terms of coordinates, rotations are most easily expressed by breaking them up into two operations. First, a rotation around the origin is given by
These matrices are the orthogonal matrices (i.e. each is a square matrix  whose transpose is its inverse, i.e. ), with determinant 1 (the other possibility for orthogonal matrices is −1, which gives a mirror image, see below). They form the special orthogonal group SO(2).
A rotation around c can be accomplished by first translating c to the origin, then performing the rotation around the origin, and finally translating the origin back to c. That is,
or in other words,
Alternatively, a rotation around the origin is performed, followed by a translation:
A rotation can be seen as a composite of two non-parallel reflections.