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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 |
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Answer» Reflexive, symmetric but not Transitive 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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