Math & Data Science Q&A - Get instant answers from our AI, GaussTheBot, that are verified by human experts
First time here? Checkout the FAQs!

*Math Image Search only works best with zoomed in and well cropped math screenshots. Check DEMO


Courses | MyLinks On Acalytica | Social Proof | Web Analytics | SEO Reports | Email Marketing | Wellness4Entrepreneurs

0 like 0 dislike
Let \(A, B\), and \(C\) be \(n \times n\) matrices.

a) If \(A^{2}\) is invertible, show that \(A\) is invertible.
[NOTE: You cannot naively use the formula \((A B)^{-1}=B^{-1} A^{-1}\) because it presumes you already know that both \(A\) and \(B\) are invertible. For non-square matrices, it is possible for \(A B\) to be invertible while neither \(A\) nor \(B\) are (see the last part of the previous Problem 41).]
b) Generalization. If \(A B\) is invertible, show that both \(A\) and \(B\) are invertible.
If \(A B C\) is invertible, show that \(A, B\), and \(C\) are also invertible.
in Mathematics by Platinum (164,924 points) | 285 views

Related questions

0 like 0 dislike
1 answer
0 like 0 dislike
1 answer

Join MathsGee, where you get instant answers from our AI that are verified by human experts. We use a combination of generative AI and human experts to provide you the best answers to your questions. Ask a question now!

On the MathsGee, you can:

1. Get instant answer to your questions

2. Get expert-verified answers

3. Vote on questions and answers

4. Tip your favorite community members

5. Join expert live video sessions (Paid/Free)

6. Earn points by participating

7. Start a Fundraiser

Posting on MathsGee

1. Remember the human

2. Act like you would in real life

3. Find original source of content

4. Check for duplicates before publishing

5. Read the community guidelines

MathsGee Rules

1. Answers to questions will be posted immediately after moderation

2. Questions will be queued for posting immediately after moderation

3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.

MathsGee Android Q&A

MathsGee Android Q&A