Find the value of the determinant of the n x n matrix A_n with main diagonal entries all 0 and all others 1. Try to find a formula for this. Try to prove it by induction. Interpret A₃ and A₄ as incidence matrices (as in Problem Set 7.1 but without the minuses) of a triangle and a tetrahedron, respectively; similarly for an n-simplex, having n vertices and n(n - 1)/2 edges (and spanning R^n-1, n = 5, 6, · · ·).