If `A=[[1, 0 ,2 ],[0 ,2 ,1],[2, 0 ,3]]`, prove that `A^3-6A^2+7A+2I=0`

Explanation

To prove that \( A^3 - 6A^2 + 7A + 2I = 0 \) for the matrix

\[ A = \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix}, \]

we will calculate \( A^2 \), \( A^3 \), \( 6A^2 \), \( 7A \), and \( 2I \) step by step.

...