1. The problem statement, all variables and given/known data Let LU and L'U' be two LU decompositions for an invertible matrix. Prove L=L' and U=U', thus the LU decomposition for an invertible matrix is unique. 2. Relevant equations 3. The attempt at a solution I honestly do not really know what to do. I suppose I could consider something with the diagonals being equal and try to show that the entries would be the same for the identity matrix, but I'm not sure how to approach any of this.