If `a , b , c` are non-zero real numbers and if the system of equations `(a-1)x=y+z` `(b-1)y=z+x` `(c-1)z=x+y` has a non-trivial solution, then `ab+bc+ca` equals to (A) `abc` (B) `a^2 - b^2 + c^2` (C) `a+b -c` (D) None of these

Explanation

To solve the given system of equations for non-trivial solutions, we can express the equations in a matrix form and find the determinant. Let's go through the steps systematically.

### Step 1: Write the system of equations in standard form

The system of equations is given as:

1. \((a-1)x = y + z\)
2. \((b-1)y = z + x\)
...