Let S be a set of all square matrices of order 2. If a relation R defined on set S such that
AR B ⇒ AB = BA, then identify the type of relation of R (A, B ∈ S) among reflexive, symmetric and transitive.
Text Solution
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Reflexive and symmetric but not transitive
Sol. Reflexive Relation :-
A.A = A.A for 
, so Relation is Reflexive Relation
Symmetric Relation :-
A.B = BA ⇒ BA = AB 
A,B ∈ S, so Relation is Symmetric Relation
Transitive Relation :-
AB = BA, BC = CB ⇒ AC = CA Not True, 
A,B,C ∈ S
for example 
, 
, 
⇒ AB = BA, BC = CB but AC ≠ CA
so Relation is not Transitive Relation
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