Diagonalization & Matrix Powers · Challenge problem

A control system's feedback gain matrix is $A = \begin{pmatrix}2 & 1\\2 & 3\end{pmatrix}$. The system's stability polynomial requires the matrix $f(A) = A^3 - 3A^2 + 2A$. Using the eigenvalues of $A$ to compute $f(A)$, find its entry in row 1, column 2.