A square of side 1 unit, specifically the unit square defined by O(0,0), I(1,0), K(1,1), J(0,1). It can be used to identify the linear map from a matrix or find the matrix if the linear map is known because the images of points I and J form the columns of the matrix which performs that transformation. For example, in a rotation of 90° clockwise (about the origin), the image of I is (0,−1) and the image of J is (1,0) so the matrix is $\left(\begin{array}{cc}0& 1\\ -1& 0\end{array}\right)$. If a matrix of a transformation is $\left(\begin{array}{cc}1& 3\\ 0& 1\end{array}\right)$ then the image of I is just the first column, i.e. (1,0), so it has not moved, and the image of J is (3,1), so the transformation is a shear parallel to the x-axis which moves (0,1) to (3,1).