The rationale peripheral to the contents of this note is absolutely a new one that targets towards an area, not previously attempted one, in the vast field of matrix algebra. A new array of numerical figures, may be complex also, lies in the fact that in the matricinal construction wherein each row vector is always perpendicular to its corresponding column vector resulting in to an array/ matrix of three pair-wise perpendicular vectors. This system, in this note, has been treated in algebraic fairness with depicting a 3-D geometrical structure/s and their related characteristics. The extension to this finite system ends with enhancing glimpses to higher dimensions.