In micro-electro-mechanical systems (MEMS), noise interference poses significant challenges to the reliability and performance of sensors. This study explores the role of matrix analysis in addressing these challenges, focusing on linear combinations of idempotent and (k+1)-potent matrices. The proposed methodology involves the introduction of a matrix T = αA + βB, where A is idempotent, B is (k+1)-potent, and (α, β) are non-zero complex numbers. The central aim of this study is to derive the necessary and sufficient conditions for T to be involutive, a property that is critical for the successful removal of noise in MEMS applications. Through a rigorous theoretical analysis, we establish these conditions and present them as actionable criteria, supported by lemmas and theorems. The results of this study contribute to a more profound comprehension of matrix interactions and offer valuable insights for the enhancement of MEMS design. This work establishes a theoretical framework integrating matrix algebra with applied engineering, thereby paving the way for the development of enhanced noise mitigation strategies in the field of MEMS technology.