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[[1,-1],[2,3]] = [[1,0],[0,1]] A, R2 rar...

`[[1,-1],[2,3]] = [[1,0],[0,1]] A, R_2 rarr R_2 - 2R_1` gives

A

`[[1,-1],[0,1]]=[[1,0],[-2,1]] A`

B

`[[1,-1],[0,5]]=[[1,0],[-2,1]]A`

C

`[[1,-1],[0,5]]=[[1,0],[2,1]] A`

D

`[[1,-1],[0,5]]=[[1,0],[-2,0]]A`

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