JEE Mains · Maths · STD 12 - 1. relation and function
Define a relation \(R\) over a class of \(n \times n\) real matrices \(A\) and \(B\) as \("ARB\) iff there exists a non-singular matrix \(P\) such that \(PAP ^{-1}= B "\) Then which of the following is true?
- A \(R\) is symmetric, transitive but not reflexive.
- B \(R\) is reflexive, symmetric but not transitive
- C \(R\) is an equivalence relation
- D \(R\) is reflexive, transitive but not symmetric
Answer & Solution
Correct Answer
(C) \(R\) is an equivalence relation
Step-by-step Solution
Detailed explanation
\(A\) and \(B\) are matrices of \(n \times n\) order ARB iff there exists a non singular matrix \(P (\operatorname{det}( P ) \neq 0)\) such that \(PAP ^{-1}= B\) For reflexive \(ARA \Rightarrow PAP ^{-1}= A \quad \ldots(1)\) must be true for \(P = I ,\) Eq.(1) is true so \('R'\)…
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