Let M denote the set of all 3 times 3 non-sin | vedclass

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(A) $1$. Reflexivity: For any matrix $A \in M$,$AA = AA$ holds true. Thus,$(A, A) \in R$. So,$R$ is reflexive.$2$. Symmetry: If $(A, B) \in R$,then $A

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Reflexive,symmetric but not transitive

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(A) $1$. Reflexivity: For any matrix $A \in M$,$AA = AA$ holds true. Thus,$(A, A) \in R$. So,$R$ is reflexive.$2$. Symmetry: If $(A, B) \in R$,then $AB = BA$. This implies $BA = AB$,which means $(B, A) \in R$. So,$R$ is symmetric.$3$. Transitivity: Let $(A, B) \in R$ and $(B, C) \in R$. This means $AB = BA$ and $BC = CB$. Does $AC = CA$? Matrix multiplication is not generally commutative. For example,if $A$ is a diagonal matrix,$B$ is a matrix that commutes with $A$,and $C$ is a matrix that commutes with $B$,$A$ and $C$ do not necessarily commute. Thus,$R$ is not transitive.

Let $M$ denote the set of all $3 \times 3$ non-singular matrices. Define the relation $R$ by $R = \{ (A,B) \in M \times M : AB = BA \}$. Then $R$ is-

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