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?
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?
- [JEE MAIN 2021]
- 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
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