Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 3 / 19H / b

For every probability vector $x$, antisymmetry gives $x^{T}Ax=0$. Applying the minimax inequalities with the same strategy on both sides shows the lower value is at most zero and the upper value at least zero; transposition also changes the value to its negative. Hence the value is zero.