1.

Let M be a set of (2 xx 2) non-singular matrices and R be a relation defined on set M such that R = {(A, B), A, B in M, A is inverse of B} then R is

Answer»

Reflexive, symmetric but not Transitive
Reflexive, Transitive but not symmetric
Neither reflexive nor Transitive
Transitive, symmetric but not reflexive

Solution :`(A,A) in R` because it is not mecessary that each matrix is inverse of its self.
Let `(A, B) in R IMPLIES A & B` are inverse of each other.
`implies AB = I = BA`
`implies BA = AB implies (B,A) in R`
Now, Let `(A, B) in R implies AB = L = BA ""....(1)`
`(B,C) in R implies BC = l = CB "".....(2)`
From (1) & (2) (AB)(BC) = I
`AB^(2)C = I`
It is CLEAR that `AB^(2)C = I` is `AC = I`, if, `B^(2) = I`
Which not possible of each matrix.


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