Using elementary transformations, find the inverse of the matrix`[[2 ,1],[ 4, 2]]`

Explanation

Let `A=[[2 ,1],[ 4, 2]]`

`A=IA`

`[[2 ,1],[ 4, 2]]=[[1,0],[0,1]].A`


`R_1->R_1/2`

`[[1 ,1/2],[ 4, 2]]=[[1/2,0],[0,1]].A`


`R_2->R_2-4R_1`

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


Since R has all numbers zero,
Thus inverse of matrix A does not exist.