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Define a relation \(R\) over a class of \(n \times n\) real matrices \(A\) and \(B\) as \(ARB\) iff there exists a non-s…

Q1

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 \(P A P^{-1}=B\). Then which of the following is true?

[JEE Main 2021, 18 Mar (Shift 2)]

a

\(R\) is reflexive, symmetric but not transitive

b

\(R\) is symmetric, transitive but not reflexive

c

\(R\) is reflexive, transitive but not symmetric

d

\(R\) is an equivalence relation

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