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Using elementary transformations, find the inverse of the matrix`[[2, 1],[ 1, 1]]`

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Given A=`[[2, 1],[ 1, 1]]`
`A=IA`
`[[2, 1],[ 1, 1]]=[[1,0],[0,1]].A`
`R_1=R_1-R_2`
`[[1,0],[1,1]]=[[1,-1],[0,1]].A`
`R_2=R_2-R_1`
`[[1,0],[0,1]]=[[1,-1],[-1,2]].A`
`I=A.A^(-1)`
...
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