<p>This paper defines a total order relation of reduced biquaternions. Based on this order relation, new rb-norms of reduced biquaternion vectors and reduced biquaternion matrices are given. Meanwhile, some algebraic properties of the Moore-Penrose inverse are discussed, and the concepts and existence conditions of the group inverse and the core inverse are introduced. The least squares solution of the reduced biquaternion system is defined, and the expression of the solution is given. In addition, a perturbation analysis of the Moore-Penrose inverse of the reduced biquaternion matrix is carried out, and the perturbation results are applied to the perturbation analysis of the least squares solution, and then the perturbation bounds of the least squares solution are obtained.</p>