On the invertibility of $3\times 3$ matrix $A$ with $A^3 −A^2 + 2A−3I = 0$

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Prove that $A$ is invertible whenever $A$ is a $3\times3$ matrix with $$A^3 −A^2 + 2A−3I = 0.$$

This is another past exam paper question I'm stuck on.