A Note on the Application of Identity Matrix

Objectives: The Identity Matrix is an important notion in linear algebra with various applications across computational and mathematical domains. The objective of the paper is to introduce a novel method for transposing matrices by utilizing the properties of Identity Matrix as agent. Method: In the proposed method, the input matrix performs Sum of Product (SOP) operations with the Identity Matrix gives the transpose. This involves describing specific mathematical operations that exploit the properties of the Identity Matrix to achieve matrix transpose. Findings: The results show that the Identity Matrix can be used to transpose binary, non- binary and complex matrices. The paper explores results obtained through empirical studies. The result shows that the algorithm runs in polynomial time. Novelty: The case study explores the application of the Identity Matrix for transposing the binary, non- binary and complex matrices with the support of examples and implementation. The uniqueness of the method is its competence to transpose matrix by operating the Sum of Product (SOP) structure. The method of matrix transpose by briefing Identity Matrix as the agent can be applied to develop a way of research to address artificial intelligence problems. Keywords: Agent­ Based Simulation, Binary Matrix, Complex Matrix, Identity Matrix, Matrix Transpose, Sum of Product