MathNet 2018-part-05 — 181 problems (EN–VI) Question 98

Let $x_1$, $x_2$, $x_3$, $y_1$, $y_2$, $y_3$ be real numbers in $[-1, 1]$. Find the maximum value of
$$
(x_1y_2 - x_2y_1)(x_2y_3 - x_3y_2)(x_3y_1 - x_1y_3)
$$