WBJEE · Maths · Sets and Relations
In the set of all \(3 \times 3\) real matrices a relation is defined as follows. A matrix \(A\) is related to a matrix \(B,\) if and only if there is a non-singular \(3 \times 3\) matrix \(P,\) such that \(B=P^{-1} A P .\) This relation is
- A reflexive, symmetric but not transitive
- B reflexive, transitive but not symmetric
- C symmetric, transitive but not reflexive
- D an equivalence relation
Answer & Solution
Correct Answer
(D) an equivalence relation
Step-by-step Solution
Detailed explanation
Let the relation defined as \(R=\left\{(A, B) \mid B=P^{-1} A P\right\}\) For reflexive, \(A=I^{-1} A l\) \(\Rightarrow (A, A) \in R\) \(\Rightarrow R\) is reflexive For symmetric \(\operatorname{Let}(A B) \in R\) \(\because\) \(B=P^{-1} A P\)…
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