Let A be an invertible matrix. Show that (An)?l = (A?1) n

Chapter 2, Problem 21E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Problem 21E

Let A be an invertible matrix. Show that (An)‒l = (A‒1) n whenever n is a positive integer.

Questions & Answers

QUESTION:

Problem 21E

Let A be an invertible matrix. Show that (An)‒l = (A‒1) n whenever n is a positive integer.

ANSWER:

Solution

In this question we have to prove that .

Step 1

Taking Left hand side (L.H.S)

Put   we get ,

=>

Now, taking right hand side (R.H.S)

Put  we get ,

=>

So, L.H.S = R.H.S

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back