Let A be a nonsingular n n matrix, and suppose that A = L1D1U1 = L2D2U2,

Question:

Let A be a nonsingular n × n matrix, and suppose that A = L1D1U1 = L2D2U2, where L1 and L2 are lower triangular, D1 and D2 are diagonal, U1 and U2 are upper triangular, and L1, L2, U1, U2 all have 1's along the diagonal. Show that L1 = L2, D1 = D2, and U1 = U2.