Fiven the matrix `A= [[-1,3,5],[1,-3,-5],[-1,3,5]]` and X be the solution set of the equation `A^(x)=A,` where `x in N -{1}`. Evaluate `prod((x^(3)+1)/(x^(3)-1))` where the contincued extends for all `x in X`.

Explanation

To solve the problem step by step, we will follow the instructions given in the video transcript and derive the solution systematically.

### Step 1: Find the powers of matrix A

Given the matrix \( A = \begin{bmatrix} -1 & 3 & 5 \\ 1 & -3 & -5 \\ -1 & 3 & 5 \end{bmatrix} \).

First, we need to compute \( A^2 \):

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