Cayley-Hamilton Theorem 1; An approach considering matrices whose components are matrices

Cayley-Hamilton Theorem is an important theorem. It states that every square matrix A satisfies its own characteristic polynomial. We prove the theorem in three different approaches. In this first video, we prove considering matrices whose components are polynomials in the matrix A. In the second video, we prove considering R-module, here R is a polynomial ring, In the last third video, we prove considering polynomials whose coefficients are matrices.