Mathematics Exam > Mathematics Questions > If A and B are two non-zero square matrices s...
Start Learning for Free
If A and B are two non-zero square matrices such that AB = 0, then
- a)both A and B are singular
- b)either A or B is singular
- c)neither A nor B is singular
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If A and B are two non-zero square matrices such that AB = 0, thena)bo...
Explanation:
To understand why option B is the correct answer, let's analyze the given information step by step.
Given: A and B are two non-zero square matrices such that AB = 0.
Now, let's consider the possibilities for the singularity of matrices A and B.
1. If A is non-singular:
If A is non-singular, it means that A has an inverse denoted as A^(-1). Multiplying both sides of the equation AB = 0 by A^(-1), we get:
A^(-1) * (AB) = A^(-1) * 0
B = 0
Here, we obtain B = 0, indicating that B is a zero matrix. However, the given information states that B is a non-zero matrix, which contradicts the assumption that A is non-singular. Therefore, A cannot be non-singular.
2. If B is non-singular:
If B is non-singular, it means that B has an inverse denoted as B^(-1). Multiplying both sides of the equation AB = 0 by B^(-1), we get:
A * (B * B^(-1)) = 0
A * I = 0
A = 0
Here, we obtain A = 0, indicating that A is a zero matrix. However, the given information states that A is a non-zero matrix, which contradicts the assumption that B is non-singular. Therefore, B cannot be non-singular.
From the above analysis, we can conclude that neither A nor B can be non-singular. Hence, the correct answer is option B: either A or B is singular.
Conclusion:
The correct answer is option B - either A or B is singular. This conclusion is reached by analyzing the possibilities for the singularity of matrices A and B based on the given information AB = 0.
To understand why option B is the correct answer, let's analyze the given information step by step.
Given: A and B are two non-zero square matrices such that AB = 0.
Now, let's consider the possibilities for the singularity of matrices A and B.
1. If A is non-singular:
If A is non-singular, it means that A has an inverse denoted as A^(-1). Multiplying both sides of the equation AB = 0 by A^(-1), we get:
A^(-1) * (AB) = A^(-1) * 0
B = 0
Here, we obtain B = 0, indicating that B is a zero matrix. However, the given information states that B is a non-zero matrix, which contradicts the assumption that A is non-singular. Therefore, A cannot be non-singular.
2. If B is non-singular:
If B is non-singular, it means that B has an inverse denoted as B^(-1). Multiplying both sides of the equation AB = 0 by B^(-1), we get:
A * (B * B^(-1)) = 0
A * I = 0
A = 0
Here, we obtain A = 0, indicating that A is a zero matrix. However, the given information states that A is a non-zero matrix, which contradicts the assumption that B is non-singular. Therefore, B cannot be non-singular.
From the above analysis, we can conclude that neither A nor B can be non-singular. Hence, the correct answer is option B: either A or B is singular.
Conclusion:
The correct answer is option B - either A or B is singular. This conclusion is reached by analyzing the possibilities for the singularity of matrices A and B based on the given information AB = 0.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer?
Question Description
If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer?.
If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Solutions for If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If A and B are two non-zero square matrices such that AB = 0, thena)both A and B are singularb)either A or B is singularc)neither A nor B is singulard)None of theseCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup