Suppose that the positive definite matrix A has the Cholesky factorization A = LLt and also the

Question:

Suppose that the positive definite matrix A has the Cholesky factorization A = LLt and also the factorization A = LDLt, where D is the diagonal matrix with positive diagonal entries d11, d22, . . ., dnn.
Let D1/2 be the diagonal matrix with diagonal entries√d11, √d22, . . . ,√dnn.
a. Show that D = D1/2D1/2.
b. Show that L = LD1/2.