Exercise 19, § 3

If $U$ is a square matrix of order $n$, $\Delta$ its determinant, $\Delta_p$ the determinant of the $p$-th exterior power of $U$ (Alg., Chapter III, § 6, No. 3), now prove that one has:

(use Exercise 11 of Alg., Chapter III, § 6, and Exercise 17 a) above).