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Answer:
Explanation: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.
If A is a given n×n matrix and In is the n×n identity matrix, then the characteristic polynomial of A is defined as[7]
{\displaystyle p(\lambda )=\det(\lambda I_{n}-A)~,}p(\lambda )=\det(\lambda I_{n}-A)~,
where det is the determinant operation and λ is a variable for a scalar element of the base ring. Since the entries of the matrix {\displaystyle (\lambda I_{n}-A)}{\displaystyle (\lambda I_{n}-A)} are (linear or constant) polynomials in λ, the determinant is also an n-th order monic polynomial in λ. The Cayley–Hamilton theorem states that if one defines an analogous matrix equation, p(A), consisting of the replacement of the scalar variable λ with the matrix A, then this polynomial in the matrix A results in the zero matrix,
{\displaystyle p(A)=0.}p(A)=0.