7. If D is given below, show that DA, AD, and A + D are P-matrices, where A is given in Prob. 6. This illustrates (i) and (5) of Theorem 11.2.2.

D =

$$

\begin{bmatrix}

1 & 0 & 0 \\

0 & 3 & 0 \\

0 & 0 & 5

\end{bmatrix}

$$