Using elementary transformations, find the inverse of the matrices`[[2, 5],[ 1, 3]]`

Explanation

Let A=`[[2, 5],[ 1, 3]]`

`A=I.A`

`[[2, 5],[ 1, 3]]=[[1,0],[0,1]].A`

`R_1->R_1-R_2`

`[[1,2],[1,3]]=[[1,-1],[0,1]].A`

`R_2->R_2-R_1`

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

`R_1->R_1-2R_2`

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