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1.Relation and Function
normal
Let $M$ denotes 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-
A
Reflexive, symmetric but not transitive
B
Reflexive, symmetric $\&$ transitive
C
Reflexive, transitive but not symmetric
D
Neither reflexive nor symmetric nor transitive
Solution
Reflexive because $\mathrm{A}^{2}=\mathrm{A}^{2}$
symmetric because $A B=B A \Rightarrow B A=A B$
not transitive because $A B=B A$
and ${\rm{BC}} = {\rm{CB}} \Rightarrow {\rm{AC}} = {\rm{CA}}$
Standard 12
Mathematics
