证明：
$$
\left|\begin{array}{lll}
a x+b y & a y+b z & a z+b x \\
a y+b z & a z+b x & a x+b y \\
a z+b x & a x+b y & a y+b z
\end{array}\right|=\left(a^3+b^3\right)\left|\begin{array}{lll}
x & y & z \\
y & z & x \\
z & x & y
\end{array}\right|
$$
$\text{A.}$
$\text{B.}$
$\text{C.}$
$\text{D.}$