If B is a non-singular matrix and A is a square matrix, then the value of det (B^$$-$$1 AB) is equal to

If a $$\ne$$ b $$\ne$$ c, then one value of x which satisfies the equation $$\left| {\matrix{ 0 & {x - a} & {x - b} \cr {x + a} & 0 & {x - c} \cr {x + b} & {x + c} & 0 \cr } } \right| = 0$$ is given by

The equations $$x + 2y + 3z = 1$$, $$2x + y + 3z = 2$$, $$5x + 5y + 9z = 4$$

What is the value of the determinant

$$\left| {\matrix{ 1 & 1 & 1 \cr 1 & {1 + xyz} & 1 \cr 1 & 1 & {1 + xyz} \cr } } \right|$$ ?