3. Problem 3 Let A, B be n x n matrices such that A is invertible and B is not invertible. Is it true that AB is always non-invertible? If false, give an example, if true, argue why.
3. Problem 3 Let A, B be n x n matrices such that A is invertible and B is not invertible. Is it true that AB is always non-invertible? If false, give an example, if true, argue why.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Answer problem 3
![### Matrix Problems
**(a)**
\[
\begin{pmatrix}
-5 & 1 \\
-6 & 1
\end{pmatrix}
\]
**(b)**
\[
\begin{pmatrix}
1 & -2 & 3 \\
2 & -5 & 10 \\
0 & 0 & 1
\end{pmatrix}
\]
**(c)**
\[
\begin{pmatrix}
1 & 2 & 1 \\
1 & 0 & 1 \\
1 & 1 & 1
\end{pmatrix}
\]
---
### Problem 3
Let \( A, B \) be \( n \times n \) matrices such that \( A \) is invertible and \( B \) is not invertible. Is it true that \( AB \) is always non-invertible? If false, give an example, if true, argue why.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0f3171b-001d-4e71-b013-5e26782f20a2%2Ff8f31f4b-3e14-4c59-8096-ea79643242b1%2F45qp4ri_processed.png&w=3840&q=75)
Transcribed Image Text:### Matrix Problems
**(a)**
\[
\begin{pmatrix}
-5 & 1 \\
-6 & 1
\end{pmatrix}
\]
**(b)**
\[
\begin{pmatrix}
1 & -2 & 3 \\
2 & -5 & 10 \\
0 & 0 & 1
\end{pmatrix}
\]
**(c)**
\[
\begin{pmatrix}
1 & 2 & 1 \\
1 & 0 & 1 \\
1 & 1 & 1
\end{pmatrix}
\]
---
### Problem 3
Let \( A, B \) be \( n \times n \) matrices such that \( A \) is invertible and \( B \) is not invertible. Is it true that \( AB \) is always non-invertible? If false, give an example, if true, argue why.
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