Exercise 8 5 5 Use the following steps to prove that det AT det A 1 First write PA LU as I did in definition 8 3 1 Then take the transpose of both sides 2 Now take the determinant of your equation with four terms Analyze which determinants you know which are simpl and which remain to be thought about 3 At the end lots of things should cancel and you should get det A det U det AT