TITLE: Is the determinant of a row reduced matrix equal to the determinant of the original matrix?
QUESTION [6 upvotes]: Prove or disprove:
 If R is the reduced row echelon form of A, then det A = det R. where A is an n x n matrix.

REPLY [2 votes]: Well, I'm not sure about "proving" this, but a contradiction to your statement: 
If A = $\begin{bmatrix}
17 & 0 \\
0 & 17 
\end{bmatrix}$, then $det(A)$ = $17^2$ 
If B = $\begin{bmatrix}
1 & 0 \\
0 & 1 
\end{bmatrix}$, then $det(A)$ = $1^2$  = 1
Also, B is the reduced echelon form of A ... therefore the determinant of a matrix and its reduced echelon form is not necessarily the same.