Finding determinant using Gaussian elimination

Question

I converted given matrix to an upper triangular matrix and my goal is finding determinant. But how to backtrack original determinant from upper triangle matrix. in other words, I swapped row , multiplied by some number, subtract one row from another raw so how they will affect determinant ?

Answer 1

Swapping two rows will multiply the determinant by $-1$.

Multiplying a row by some number $a$ will multiply the determinant by $a$, so to get the determinant of the original matrix, you will need to multiply the determinant you find by $a^{-1}$.

Adding some multiple of one row to some other row does not change the determinant.