Question

state and proof every square matrix satisfies its characteristics equation​

Answer 1

Answer:

In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex field) satisfies its own characteristic equation.

Answer 2

Step-by-step explanation:

The Cayley-Hamilton is used to demonstrate the finite-dimensional true division algebras are classified (although there may be many other evidence). There is a very important theorem by Procesi deriving from the Cayley-Hamilton theorem all the polynomial identities of the matrix ring.

The characteristic equation of the matrix a is defined as - det(A − λI) = 0

Where, Eigenvalues λ of a are the roots of characteristic equation. that are associated eigenvectors of a and are thus, the nonzero solutions of the equation (A − λI)x = 0.