When a shape is traced out in a clockwise direction, its
image after a reflection is traced out in an anti-clockwise
direction. In every other way the object and its image are
the same. What has changed is its sense.
In the same way,
a right glove or shoe is in the opposite sense to its partner,
the left glove or shoe. It is this property of a reflection
which distinguishes it from all the other common transformation
such as translation rotations and enlargements.
determinant of a matrix is negative, the transformation it
produces will change the sense of any shape on which it operates.