translation from Hebrew: let $A=(a_{ij})_{n\cdot n}$ prove that the determinants of the following matrices is as follows: $(u_1+u_2+...+u_n)det(A)$. I proposed using the additive property of the determinant, my friend corrected me and said that isn't possible due to the fact that every pair of matrices has 2 different rows from each other... thanks for helping!