Let $M$ be the set of all $3 \times 3$ matrices with real entries. Consider the relation $R$ on $M$ given by $R=\{(A, B) \in M \times M: \operatorname{det}(A-B)$ is an integer $\}$. Which one of the following statements is Correct?

• A

  $R$ is reflexive, but neither symmetric nor transitive.
• Correct answer
  B

  $R$ is reflexive and symmetric, but not transitive.
• C

  $R$ is an equivalence relation.
• D

  $R$ is symmetric and transitive, but not reflexive.

Hence, the correct answer is option: 'B'.