no because for any elementary row operation you want to do, doesn't matter when reducing the matrix into the echelon form, but it does affect the determinant, so it needs to be computed the determinant given the "intact" matrix.
I have a question here relating to getting the eigenvalues of a matrix.
The matrix is 3 x 3. Im just wondering that when you are getting the determinant of
det(I*Lambda - A). Is it ok to row reduce the matrix A first before subbing into this equation?