Let A={:((1,2),(3,4):}) and B={:((a,0),(...

Let `A={:((1,2),(3,4):})` and `B={:((a,0),(0,b)):}`, where `a,b in N`, then

A

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

B

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

C

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

D

There exist infinity may B's such that AB=BA

Verified by Experts

The correct Answer is:

D

`becauseAB=[{:(1,2b),(3a,4b):}]` and `BA=[{:(1,2a),(3b,4b):}]`
`therefore` for `AB=BA`
`a=b`

Similar Questions

Explore conceptually related problems

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 ?

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

Let A=[(2,3),(5,7)] and B=[(a, 0), (0, b)] where a, b in N . The number of matrices B such that AB=BA , is equal to

Let A={:[(1,2,3),(0,1,0)]:}andB={:[(-1,4,3),(1,0,0)]:} Find 2A +3B.

Let A=[{:(5,0,-2),(3,2,-7):}]" and B=[{:(4,-3,-6),(-1,0,4):}]. Clearly, each one of A and B is a 2xx3 matrix. Find A + B

if A'=[{:(3,4),(-1,2),(0,1):}]and B=[{:(-1,2,1),(1,2,3):}], then verify that (i) (A+B)'=A'+B'(ii) (A-B)'=A'-B'

Let A = [{:(2, b,1),(b, b^(2)+1,b),(1, b,2):}], " where "b gt 0 . Then, the maximum value of ("det"(A))/(b) is

Let A=[{:(" "2,3,5),(-1,0,4):}]" and "B=[{:(4,-2,3),(2," "6,-1):}]. Verify that A+B=B+A.

Let A={:[(2,3,5),(1,0,2),(3,4,5)]:}andA+B-4I=0 , then B is equal to