Matrices and Determinants: JEE Main 2008 Mathematics question

Let $a, b, c$ be any real numbers. Suppose that there are real numbers $x, y, z$ not all zero such that $x=cy+bz,$ $y=az+cx,$ and $z=bx+ay.$ Then ${a^2} + {b^2} + {c^2} + 2abc$ is equal to :