Find the value of the determinant of the n x n matrix and 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 Rn–1, n = 5, 6 . . .)