Which one of the following matrices can be obtained by performing...

Any matrix obtained by performing elementary row transformations on the identity matrix is equivalent to the identity matrix, which means it must be non-singular (invertible). Therefore, its determinant must be non-zero.

Evaluating the determinant of the matrix in option (A):
$\begin{vmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{vmatrix} = 0$

Evaluating the determinant of the matrix in option (B):
$\begin{vmatrix} 1 & 1 & 1 \\ 2 & 3 & 4 \\ 1 & 2 & 1 \end{vmatrix} = 1(3 - 8) - 1(2 - 4) + 1(4 - 3) = -5 + 2 + 1 = -2 \neq 0$

Evaluating the determinant of the matrix in option (C):
$\begin{vmatrix} 1 & 1 & 1 \\ 2 & 3 & 4 \\ 2 & 5 & 8 \end{vmatrix} = 1(24 - 20) - 1(16 - 8) + 1(10 - 6) = 4 - 8 + 4 = 0$

Evaluating the determinant of the matrix in option (D):
$\begin{vmatrix} 1 & 1 & 1 \\ -1 & 1 & 2 \\ 0 & 2 & 3 \end{vmatrix} = 1(3 - 4) - 1(-3 - 0) + 1(-2 - 0) = -1 + 3 - 2 = 0$

Since only the matrix in option (B) has a non-zero determinant, it is the only one that can be obtained from the identity matrix by elementary row transformations.

Answer: $\begin{bmatrix} 1 & 1 & 1 \\ 2 & 3 & 4 \\ 1 & 2 & 1 \end{bmatrix}$