For example multiply the unit matrix by a constant, or use a simple scalar multiplication by the unit matrix to obtain the diagonal elements of a given matrix.
For example, the matrices describing the identity mapping and the inversion are orthogonal in any basis, viz the unit matrix and the negative unit matrix.
The unit matrix is a unit that provides objects for the common two, three and four dimensional vectors matrixes.
The matrix J is a signature matrix of the form where the two unit matrices do not necessarily have the same dimensions.
In the case of the unit matrix, we call either column major.