4. (16%) Factor the matrix A into a product $$XDX^{-1}$$, where D is diagonal and $$A = \begin{bmatrix} 1 & 0 & 0 \\ -2 & 1 & 3 \\ 1 & 1 & -1 \end{bmatrix}$$.

(4%) (a) X, (4%) (b) D, (4%) (c) $$X^{-1}$$. (4%) (d) Find a matrix B such that $$B^3=A$$