A =$\displaystyle \begin{bmatrix} 1 & 1 & 0 \\0 & 2 & 1 \\-4 & -11 & -4 \end{bmatrix}$

find the smallest value ofn > 0such that

I need help on this question, I am suppose to solve it using matlab, however, I dont even know how to solve this on paper, let alone matlab, any suggestions or help appreciated.

I have tried to to it like this

$\displaystyle A^{-1}A^{n} =IA^{-1} $

$\displaystyle n = IA^{-1} $

to get n, and matlab gives me,

$\displaystyle \begin{bmatrix} -3 & -4 & -1 \\4 & 4 & 1 \\-8 & -7 & -2 \end{bmatrix}$

so is n = 1? Is this correct?