2012-37.md

course	course_year	question_number	tags	title	year
Linear Algebra	IB	37	IB 2012 Linear Algebra	Paper 2, Section I, $1 F$	2012

Define the determinant $\operatorname{det} A$ of an $n \times n$ real matrix $A$. Suppose that $X$ is a matrix with block form

$$X=\left(\begin{array}{cc} A & B \\ 0 & C \end{array}\right) \text {, }$$

where $A, B$ and $C$ are matrices of dimensions $n \times n, n \times m$ and $m \times m$ respectively. Show that $\operatorname{det} X=(\operatorname{det} A)(\operatorname{det} C)$.