The original matrix is:
\begin{bmatrix} 1 &2 &0 &1 \\ 3 &3 &3 &9 \\ 1 & 4 & 1 &4 \\ 1 & 1 & 2 &0 \end{bmatrix}
Every time I reduced this to row echelon form, I got $\dfrac{1}{48}$ as the determinant when the actual determinant is $48$. Here are the row operations.
The rows that I have highlighted are the ones that change the determinant since we are changing a row by a factor. All the other operations don't change the determinant and we never switch rows here.
So we get $\det(A) = \dfrac{-1}{3}\times\dfrac{1}{3}\times\dfrac{-3}{16}\times 1 \text{ (entries along diagonal)} = \dfrac{1}{48}$. But the actual determinant is $48$. Where have I went wrong? I did the row operations a couple of times but I am making the same mistake.