2013-38.md

course	course_year	question_number	tags	title	year
Linear Algebra	IB	38	IB 2013 Linear Algebra	Paper 1, Section I, E	2013

What is the adjugate of an $n \times n$ matrix $A$ ? How is it related to $A^{-1}$ ? Suppose all the entries of $A$ are integers. Show that all the entries of $A^{-1}$ are integers if and only if $\operatorname{det} A=\pm 1$.