If `abc=p` and `A=[(a,b,c),(c,a,b),(b,c,a)]`, prove that A is orthogonal if and only if a, b, c are the roots of the equation `x^(3) pm x^(2)-p=0`.

Explanation

To prove that the matrix \( A = \begin{pmatrix} a & b & c \\ c & a & b \\ b & c & a \end{pmatrix} \) is orthogonal if and only if \( a, b, c \) are the roots of the equation \( x^3 \pm x^2 - p = 0 \), we will follow these steps:

### Step 1: Understand Orthogonality
A matrix \( A \) is orthogonal if \( A A^T = I \), where \( A^T \) is the transpose of \( A \) and \( I \) is the identity matrix.

### Step 2: Find the Transpose of Matrix \( A \)
The transpose of matrix \( A \) is:
\[
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