Let \(A\) be a \(3\times 3\) real matrix such that \({A}^{2}(A-2I)-4(A-I)=O\) , where \(I\) and \(O\) are the identity a…

Let \(A\) be a \(3\times 3\) real matrix such that \({A}^{2}(A-2I)-4(A-I)=O\) , where \(I\) and \(O\) are the identity and null matrices, respectively. If \({A}^{5}=\alpha {A}^{2}+\beta A+\gamma I\), where \(\alpha ,\beta\) and \(\gamma\) are real constants, then \(\alpha +\beta +\gamma\) is equal to:

[JEE Main 2025, 2 Apr (Shift 2)]