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If A=[{:(2,-3),(-1,2):}] then A^(-1)=...

If `A=[{:(2,-3),(-1,2):}]` then `A^(-1)=`

A

`[{:(2,-3),( -1,2):}]`

B

`[{:(2,3),( 1,2):}]`

C

`[{:( -1,2),(2,-3):}]`

D

`[{:( 1,2),(2,3):}]`

Text Solution

Verified by Experts

The correct Answer is:
B
`Let A= [{:(2,-3),(-1,2):}]`
`Now , A=IA `
`implies [{:(2,-3),(-1,2):}]=[{:(1,0),(0,1):}]A`
`implies [{:(1,-1),(-1,2):}]=[{:(1,1),(0,1):}]A R_(1) to R_(1)+R_(2)`
`implies [{:( 1,-1),( 0,1):}]=[{:(1,1),( 1,2):}]A R_(2) to R_(2) +R_(1)`
`implies [{:(1,0),( 0,1):}]=[{:(2,3),( 1,2):}]A R_(1) to R_(1) +R_(2)`
`therefore A^(-1) =[{:(2,3),( 1,2):}]`
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