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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 nonsingular matrix P …

Q1

Define a relation R over a class of \(n\times n\) real matrices A and B as "ARB iff there exists a nonsingular matrix P such that \(PA{P}^{-1}={B}^{''}\). 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 no reflexive

c

R is reflexive, transitive but not symmetric

d

R is an equivalence relation

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