# JEE Main & Advanced Mathematics Matrices Cayley-Hamilton Theorem

## Cayley-Hamilton Theorem

Category : JEE Main & Advanced

Every matrix satisfies its characteristic equation e.g. let A be a square matrix then $|A-xI|=0$is the characteristics equation of A. If ${{x}^{3}}-4{{x}^{2}}-5x-7=0$ is the characteristic equation for A, then ${{A}^{3}}-4{{A}^{2}}+5A-7I=0$.

Roots of characteristic equation for A are called Eigen values of A or characteristic roots of A or latent roots of A.

If $\lambda$ is characteristic root of A, then ${{\lambda }^{-1}}$is characteristic root of ${{A}^{-1}}$.

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