Chapter 5, Problem 12SE

Let G = $\left[\begin{array}{cc}\text{A}& \text{X}\\ 0& \text{B}\end{array}\right]$ Use formula (1) for the determinant in Section 5.2 to explain why det G = (det A)(det B). From this, deduce that the characteristic polynomial of G is the product of the characteristic polynomials of A and B.