If `S=[(0,1,1),(1,0,1),(1,1,0)]` and `A=[(b+c,c-a,b-a),(c-b,c+b,a-b),(b-c,a-c,a+b)]`
`(a, b, c ne 0)`, then `SAS^(-1)` is

Options

A. symmetric matrix
B. diagonal matrix
C. invertible matrix
D. singular matrix

Explanation

To solve the problem, we need to find \( SAS^{-1} \) where \( S = \begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} \) and \( A = \begin{pmatrix} b+c & c-a & b-a \\ c-b & c+b & a-b \\ b-c & a-c & a+b \end{pmatrix} \).

### Step 1: Calculate the Inverse of \( S \)

To find \( S^{-1} \), we first need to calculate the determinant of \( S \).

**Determinant of \( S \)**:
\[
...