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Question

Let A=[1234] and B=[a00b],a,b,ϵ N. Then

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

The correct option is D there exists infinitely many B's such that AB = BA.
A=[1234],B=[a00b]AB=[a2b3a4b]andBA=[a00b][1234]=[a2a3b4b]
AB = BA only when a = b.

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