We have classified square matrices based on the ‘Libra value’ * property in six different classes. In this note we unfold what we have found and establish about dominating properties of matrices of class 4B** and also its ring structure. It has been shown that some sets of standard form of class4B matrices satisfy commutative property under matrix multiplication. In addition to this, we describe different transformations that convert matrices of class 4B to their corresponding matrices of class 4A and vice – versa. Libra value: Libra value of a given square matrix is that constant value for the given matrix obtained by adding the all the entries of each row or column or diagonal (both leading or non-leading) as the case may be depending on the classification. Notations: (1) CJ4A (n ´ n, L (A) = ___ ) [Square Matrix of class 4A with order n ´ n and L (A) = libra value. L (A) = libra value] (2) CJ4B (n ´ n, L (A) = _____ ) [Square matrix of class 4B with order n ´ n] and L (B) = libra Value] (3) CJS4B [A symmetric matrix of CJ4B] (4) is a Null matrix (5) I is an identity matrix