Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Define a relation 
over a class of 
real matrices 
and 
as 
if there exists a non-singular matrix 
such that 
. Then which of the following is true?
A
is symmetric, transitive but not reflexive,
B
is reflexive, symmetric but not transitive
C
is an equivalence relation
D
is reflexive, transitive but not symmetric
Text Solution
Verified by ExpertsThe correct answer is:
C
JEE Main 2021
and 
are matrices of 
order & 
if there exists a non singular matrix 
such that 
For reflexive
must be true for 
, Eq. 
is true so 
is reflexive
For symmetric
is true
For 
if 
must be true
…..(iii)
From 
Can be true some 
So 
is symmetric
For transitive
is true
is true
Now 
So 
is transitive relation
Hence 
is equivalence
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