Given a square matrix A, is the determinant of A equals to the product of the diagonal elements of A after the echelon?
I know that making operations with lines change the determinant, but I did it in some matrices and all of them had the same determinant than the product of the diagonal elements of itself after echeloning.
Is this proprierty true?
Can someone give me a hint on how to prove it, if it's true?
For simplicity, let A non singular.