To apply elementary row transformations we write:
A = IA where I is the identity matrix
We proceed with operations in such a way that LHS becomes I and the transformations in I give us a new matrix such that
I = XA
And this X is called inverse of A = A-1
Note: Never apply row and column transformations simultaneously over a matrix.
So we have:
As second row of LHS contains all zeros, So by anyhow we are never going to get Identity matrix in LHS.
∴ Inverse of A does not exist.
A-1 does not exist.