Proof of an inverse Matrix

Question

I am very raw at proofs, this is only my first semester learning them and I am having trouble with this problem. How would I approach this ?

If $$ is an $ × $ matrix that satisfies the equation $ $ is $A^3 -4A^2 +3A -5I_n = 0$, Find the $A^{-1}$

Answer 1

$$A^3 -4A^2 +3A -5I_n = 0$$

Or, $$5I_n = A^3 -4A^2 +3A$$

Pre-multiplying both sides by $A^{-1}$ and dividing by $5$, $$A^{-1} = \frac{1}{5}(A^2 -4A +3I_n)$$