Find the products AB and BA to determine whether B is the multiplicative inverse of A. 12 [3²]. -[ 위 31 1 AB= BA= - 3 -3 Is R the multiplicative inverse of A2
Find the products AB and BA to determine whether B is the multiplicative inverse of A. 12 [3²]. -[ 위 31 1 AB= BA= - 3 -3 Is R the multiplicative inverse of A2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Matrix Multiplicative Inverse Exploration**
**Task:** Find the products AB and BA to determine whether matrix B is the multiplicative inverse of matrix A.
**Given Matrices:**
\[ A = \begin{bmatrix} 1 & 2 \\ 3 & 1 \end{bmatrix} \]
\[ B = \begin{bmatrix} -3 & 0 \\ -3 & -1 \end{bmatrix} \]
**Steps:**
1. Calculate the product AB.
2. Calculate the product BA.
3. Determine whether B is the multiplicative inverse by checking if both AB and BA result in the identity matrix.
**Enter your results:**
AB = \[ \boxed{} \]
BA = \[ \boxed{} \]
**Question:**
Is B the multiplicative inverse of A?
- ☐ Yes
- ☐ No
**Instructions for Calculation:**
To find if B is the inverse of A, both matrix products AB and BA should equal the identity matrix:
\[ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb76a34ef-22d3-4cb0-8af6-813d524e1e4e%2F2e3a654c-f1f5-4de7-b860-67459accc01c%2Fb2tsd3d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Multiplicative Inverse Exploration**
**Task:** Find the products AB and BA to determine whether matrix B is the multiplicative inverse of matrix A.
**Given Matrices:**
\[ A = \begin{bmatrix} 1 & 2 \\ 3 & 1 \end{bmatrix} \]
\[ B = \begin{bmatrix} -3 & 0 \\ -3 & -1 \end{bmatrix} \]
**Steps:**
1. Calculate the product AB.
2. Calculate the product BA.
3. Determine whether B is the multiplicative inverse by checking if both AB and BA result in the identity matrix.
**Enter your results:**
AB = \[ \boxed{} \]
BA = \[ \boxed{} \]
**Question:**
Is B the multiplicative inverse of A?
- ☐ Yes
- ☐ No
**Instructions for Calculation:**
To find if B is the inverse of A, both matrix products AB and BA should equal the identity matrix:
\[ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]
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