Let A =((1,2),(3,4))and B= ((a,0),(0,b))...

Let `A =((1,2),(3,4))and B= ((a,0),(0,b)), a, bin N.` Then,

A

there connot 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 many B's such that AB=BA.

Text Solution

Verified by Experts

The correct Answer is:

D

We have
`{:AB=[(a,2b),(3a,4b)]and BA=[(a,2a),(3a,4b)]:}`
Clearly, AB=BA only when a=b

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