Problem

In Exercises 31–36, mention an appropriate theore…

02:05

Problem 34 Medium Difficulty

In Exercises 31–36, mention an appropriate theorem in your explanation.
Let $A$ and $P$ be square matrices, with $P$ invertible. Show that $\operatorname{det}\left(P A P^{-1}\right)=\operatorname{det} A$

Answer

see the proof

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Algebra

Linear Algebra and Its Applications

Chapter 3

Determinants

Section 2

Properties of Determinants

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Video Transcript

okay. In this question, we want to show that determines right here is equal to determine off, eh? So how do we do this? You first separate out the products. Then it will be determines off a as a determinant four p invest. So what we do is we arranged. We rearrange. Hey, turn it off. He even this turn this all day. So pushing in the two peas? Yeah, he pilot, he in this. How's my determinant? Okay, now, Pete Pete in verse is the identity matrix Identity matrix has, like, determinants off, eh? Now, determinants off the identity matrix is just simply one. So therefore, this is just a terminus, okay?

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