Matrix zeros of polynomials

TLDR: The concepts of polynomials and matrices essentially expand and enhance the elementary arithmetic of numbers as mentioned in this paper and open up new interesting mathematical challenges which extend to new fields of mathematical explorations within university mathematics.

Abstract: The concepts of polynomials and matrices essentially expand and enhance the elementary arithmetic of numbers. Once introduced, polynomials and matrices open up new interesting mathematical challenges which extend to new fields of mathematical explorations within university mathematics. We present an aspect of a rather elementary exploration of polynomials and matrices, which offers a new perspective and an interesting matrix analogue to the concept of a zero of a polynomial. The discussion offers an opportunity for better comprehension of the fundamental concepts of polynomials and matrices. As an application we are led to the meaningful questions of linear algebra and to an easy proof of the otherwise advanced and abstract Cayley-Hamilton theorem.