Using Cayley hamilton therom to find the value of matrix

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This is the problem where I don't understand how the equations get cancelled and the answers comes out to be $A^2+A+I$. When I am doing the same thing there $7A^4$ which is't cancelled.

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I got the answer. The solution is that since, $A^3-5A^2+7A-3I=0$ by the theorem the first term becomes zero and the solution arrives when we the follow the steps.