If A=[(1,-1),(2,1)], B=[(a,1),(b,-1)] an...

If `A=[(1,-1),(2,1)], B=[(a,1),(b,-1)]` and `(A+B)^(2)=A^(2)+B^(2)+2AB`, then

A

`a=-1`

B

`a=1`

C

`b=2`

D

`b=-2`

Text Solution

Verified by Experts

The correct Answer is:

A, D

Given, `(A+B)^(2)=A^(2)+B^(2)+2AB`
or `(A+B) (A+B)=A^(2)+B^(2)+2AB`
or `A^(2)+AB+BA+B^(2)=A^(2)+B^(2)+2AB` or `BA=AB`
or `[(a,1),(b,-1)] [(1,-1),(2,1)]=[(1,-1),(2,1)][(a,1),(b,-1)]`
or `[(a+2,-a+1),(b-2,-b-1)]=[(a-b,1+1),(2a+b,2-1)]`
The corresponding elements of equal matrices are equal.
`a+2=a-b, -a+1=2 implies a=-1`
`b-2=2a+b, -b-1=1implies b=-2`
`implies a=-1, b=-2`

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