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If A=[{:(1,-1),(2,-1):}],B=[{:(a,-1),(b,...

If `A=[{:(1,-1),(2,-1):}],B=[{:(a,-1),(b,-1):}]" and "(A+B)^(2)=(A^(2)+B^(2))` then find the values of a and b.

A

a=2,b=-3

B

a=-2,b=3

C

a=1,b=4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(A+B)^2=(A^2+B^2) iff A^2+B^2+AB=(A^2+B^2) iff AB=-BA`
`AB=-BA iff [(a-b,2),(2a-b,3)]=[(-a-2,a+1),(-b+2,b-1)]`
`Now ,(a+1=2 and b-1=3) rArr (a=1 and b=4)`
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