9. Let fJj = (Vj1,"" Vjn) ERn, j = 1, ... , n, be fixed. The parallelepiped determined by the vectors fJj is the set P(fJ1, ... ,fJn ) := {hfJ1 + ... + tnfJn : tj E [0, I]}, and the determinant of the fJj's is the number det(fJ1"" ,fJn ) := det [vjkl nxn'

Prove that Vol (P(fJ1,'" ,fJn )) = I det(fJ1'''' ,fJn)l·

Check this formula for n = 2 and n = 3 to see that it agrees with the classical formulas for the area of a parallelogram and the volume of a parallelepiped.