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In the set of all 3×3 real matrices a relation is defined as follows. A matrix A is related to a matrix B if and only if there is a non-singular 3×3 matrix P such that B = P–1AP. This relation is
  • a)
    Reflexive, Symmetric but not Transitive
  • b)
    Reflexive, Transitive but not Symmetric
  • c)
    Symmetric, Transitive but not Reflexive
  • d)
    an Equivalence relation
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In the set of all 3×3 real matrices a relation is defined as fol...
R = {(A, B) | B = P–1 AP}
A = I–1AI ⇒ (A, A) ∈ R  ⇒ R is reflexive
Let (A, B) ∈ R , B = P–1AP PB = AP
⇒ PBP–1 = A ⇒ A = (P–1)–1 B(P–1)
⇒ (B, A) ∈R, ⇒ R is symmetric
Let (A, B) ∈ R, (B, C) ∈ R
A = P–1BP and B = Q–1CQ
A = P–1Q–1C QP = (QP)–1 C(QP)
⇒ (A, C) ∈R
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In the set of all 3×3 real matrices a relation is defined as fol...
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In the set of all 3×3 real matrices a relation is defined as follows. A matrix A is related to a matrix B if and only if there is a non-singular 3×3 matrix P such that B = P–1AP. This relation isa)Reflexive, Symmetric but not Transitiveb)Reflexive, Transitive but not Symmetricc)Symmetric, Transitive but not Reflexived)an Equivalence relationCorrect answer is option 'D'. Can you explain this answer?
Question Description
In the set of all 3×3 real matrices a relation is defined as follows. A matrix A is related to a matrix B if and only if there is a non-singular 3×3 matrix P such that B = P–1AP. This relation isa)Reflexive, Symmetric but not Transitiveb)Reflexive, Transitive but not Symmetricc)Symmetric, Transitive but not Reflexived)an Equivalence relationCorrect answer is option 'D'. 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 set of all 3×3 real matrices a relation is defined as follows. A matrix A is related to a matrix B if and only if there is a non-singular 3×3 matrix P such that B = P–1AP. This relation isa)Reflexive, Symmetric but not Transitiveb)Reflexive, Transitive but not Symmetricc)Symmetric, Transitive but not Reflexived)an Equivalence relationCorrect answer is option 'D'. 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 set of all 3×3 real matrices a relation is defined as follows. A matrix A is related to a matrix B if and only if there is a non-singular 3×3 matrix P such that B = P–1AP. This relation isa)Reflexive, Symmetric but not Transitiveb)Reflexive, Transitive but not Symmetricc)Symmetric, Transitive but not Reflexived)an Equivalence relationCorrect answer is option 'D'. Can you explain this answer?.
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