\(A=n^3-2n^2+2n-4=n^2\left(n-2\right)+2\left(n-2\right)=\left(n^2+2\right)\left(n-2\right)\)

A is prime,so A > 0.Moreover,\(n^2+2\ge2>0\).So n - 2 > 0.

A is prime,so one of the factor is 1 and the another is equal to A but \(n^2+2\ge2>1\).So \(n-2=1\Leftrightarrow n=3\Leftrightarrow n^2+2=11\Leftrightarrow A=11\)

Indeed,11 is prime.Hence,n = 3