If `S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(2sqrt(2))),(sqrt(3)-1)/(2sqrt(2)))], A=[(1,0),(-1,1)]` and `P=S ("adj.A") S^(T)`, then find matrix `S^(T) P^(10) S`.

Explanation

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

### Step 1: Define the Matrices
We are given two matrices:
- \( S = \begin{pmatrix} \frac{\sqrt{3}-1}{2\sqrt{2}} & \frac{\sqrt{3}+1}{2\sqrt{2}} \\ -\frac{\sqrt{3}+1}{2\sqrt{2}} & \frac{\sqrt{3}-1}{2\sqrt{2}} \end{pmatrix} \)
- \( A = \begin{pmatrix} 1 & 0 \\ -1 & 1 \end{pmatrix} \)

### Step 2: Calculate the Adjoint of Matrix A
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