The set of all appropriate matrices together with the operation of matrix multiplication is the rotation group SO(3). The matrix is a member of the three-dimensional special orthogonal group, , that is it is an orthogonal matrix with determinant 1. That it is an orthogonal matrix means that its rows are a set of orthogonal unit vectors (so they are an orthonormal basis) as are its columns, making it simple to spot and check if a matrix is a valid rotation matrix.