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?

Question

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?

R is reflexive, transitive but not symmetric

R is symmetric, transitive but not reflexive.

R is reflexive, symmetric but not transitive

R is an equivalence relation

Solution

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