Let `A=[{:(1,2),(3,4):}]and B = [{:(a,0),(0,b):}]` where a, b are natural numbers, then which one of the following is correct ?

Options

A. there cannot exist any B such that `AB = BA`
B. There exist more than one but finite number of `B`' s such that
`AB = BA`
C. there exists exactly one B such that `AB = BA`
D. there exist infinitely among `B'` s such that `AB = BA`

Answer

B

Explanation

`A = ((1,2),(3,4)), B=((a,0),(0,b))`
`rArr AB= ((a,2b),(3a,4b))`
and ` = ((a,0),(0,b))((1,2),(3,4))=((a,2a),(3b,4b))`
Hence, AB = BA only when a = b.