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Let {:A=[(1,2),(3,4)]and BA=[(a,0),(0,b)...

Let `{:A=[(1,2),(3,4)]and BA=[(a,0),(0,b)]:},a,b in N` Then,

A

there exist more than one but finite number of `B's` such that `AB=BA`

B

there exists exactly one B such that `AB=BA`

C

there exists infinitely many B's such that `AB=BA`

D

there cannot exist any B such that `AB=BA`

Text Solution

Verified by Experts

The correct Answer is:
C
`AB=[(1,2),(3,4)][(a,0),(0,b)]=[(a,2b),(3a,4b)]`
and `BA=[(a,0),(0,b)][(1,2),(3,4)]=[(a,2a),(3b,4b)]`
If `AB=BA` then `a=b`
Hence `AB=BA` is possible for infinitely many values of B's.
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