$A^{-1} and A^4$

Characteristic equation of A is $\mid A-\lambda I \mid=0$

$\lambda^3-6\lambda^2+[(4+4+4)-(1+1+1)]\lambda-\mid A \mid=0$

$\lambda^3-6\lambda^2+(12-3)\lambda-4=0$

$\lambda^3-6\lambda^2+9\lambda-4=0$

To verify Cayley-Hamilton Theorem, we need to prove that $A^3-6A^2-4I=0$

LHS=$A^3-6A^2+9A-4I$

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