1
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
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 and symmetric, but not transitive.
B
$R$ is reflexive, but neither symmetric nor transitive.
C
$R$ is an equivalence relation.
D
$R$ is symmetric and transitive, but not reflexive.
2
IAT (IISER) 2020
MCQ (Single Correct Answer)
+4
-1

$$ \text { Define binary operation * on } Q \text { by } a * b=a+b-3 \text {. The inverse of } 2 \text { with respect to * is } $$

A
4
B
2
C
3
D
5
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