The Determinant of Cubic-Matrix of order 2 and order 3: Some basic Properties and Algorithms

TL;DR

This paper introduces and visualizes the concept of determinants for 3D cubic matrices of orders 2 and 3, establishing basic properties and algorithms for their calculation.

Contribution

It defines determinants for cubic matrices of orders 2 and 3, and proves their fundamental properties, extending classical matrix determinant concepts to 3D matrices.

Findings

Determinants for cubic matrices of order 2 and 3 are defined and visualized.

Basic properties of these determinants are established and proven.

Properties of square determinants are applicable to 3D determinants.

Abstract

Based on geometric intuition, in this paper we are trying to give an idea and visualize the meaning of the determinants for the cubic-matrix. In this paper we have analyzed the possibilities of developing the concept of determinant of matrices with three indexed 3D Matrices. We define the concept of determinant for cubic-matrix of order 2 and order 3, study and prove some basic properties for calculations of determinants of cubic-matrix of order 2 and 3. Furthermore we have also tested several square determinant properties and noted that these properties also are applicable on this concept of 3D Determinants.