A square matrix is called strictly lower (upper) triangular if all entries on or above (below) the

Question:

A square matrix is called strictly lower (upper) triangular if all entries on or above (below) the main diagonal are 0.
(a) Prove that any square matrix can be uniquely written as a sum A = L + D+U, with L strictly lower triangular, D diagonal, and U strictly upper triangular.
(b) Decompose