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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.
Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.
Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.
Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.
- a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
- b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
- c)Assertion is true but Reason is false.
- d)Assertion is false but Reason is true.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In the following question, a Statement of Assertion (A) is given follo...
Explanation:
The given Assertion and Reason are related to the commutativity of a 2 x 2 matrix. Let us understand each of them in detail.
Assertion (A): If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.
This assertion states that if a 2 x 2 matrix A commutes with every 2 x 2 matrix B, then A must be a scalar matrix. To understand why this is true, let us assume that A is not a scalar matrix. Then, there exists a non-zero 2 x 2 matrix B such that AB is not equal to BA. But the assertion states that A commutes with every 2 x 2 matrix B, which contradicts our assumption. Therefore, A must be a scalar matrix.
Reason (R): A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.
This reason states that a 2 x 2 scalar matrix commutes with every 2 x 2 matrix. This is true because a scalar matrix is a matrix in which all the diagonal elements are equal and all the off-diagonal elements are zero. Therefore, when a scalar matrix is multiplied with any 2 x 2 matrix B, the product AB is equal to BA, as all the off-diagonal elements in AB and BA are zero.
Conclusion:
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
The given Assertion and Reason are related to the commutativity of a 2 x 2 matrix. Let us understand each of them in detail.
Assertion (A): If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.
This assertion states that if a 2 x 2 matrix A commutes with every 2 x 2 matrix B, then A must be a scalar matrix. To understand why this is true, let us assume that A is not a scalar matrix. Then, there exists a non-zero 2 x 2 matrix B such that AB is not equal to BA. But the assertion states that A commutes with every 2 x 2 matrix B, which contradicts our assumption. Therefore, A must be a scalar matrix.
Reason (R): A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.
This reason states that a 2 x 2 scalar matrix commutes with every 2 x 2 matrix. This is true because a scalar matrix is a matrix in which all the diagonal elements are equal and all the off-diagonal elements are zero. Therefore, when a scalar matrix is multiplied with any 2 x 2 matrix B, the product AB is equal to BA, as all the off-diagonal elements in AB and BA are zero.
Conclusion:
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
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Community Answer
In the following question, a Statement of Assertion (A) is given follo...
A scalar matrix is a square matrix in which it's diagonal elements are of equal magnitude/same value and all other elements are zero .
So a scalar matrix is a multiple of identity matrix(i.e,kI). So it follows commutative law (AB=BA or A+B=B+A)
(In the given question commutes means obeying commutative law)
So a scalar matrix is a multiple of identity matrix(i.e,kI). So it follows commutative law (AB=BA or A+B=B+A)
(In the given question commutes means obeying commutative law)
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?.
In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion(A) :If a 2 x 2 matrix commutes with every 2 x 2 matrix, then it is a scalar matrix.Reason(R) :A 2 x 2 scalar matrix commutes with every 2 x 2 matrix.a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?.
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