Chapter 2.1, Problem 11E

Let $A=\left[\begin{array}{ccc}1& 1& 1\\ 1& 2& 3\\ 1& 4& 5\end{array}\right]$ and $D=\left[\begin{array}{ccc}2& 0& 0\\ 0& 3& 0\\ 0& 0& 5\end{array}\right]$. Compute AD and DA. Explain how the columns or rows of A change when A is multiplied by D on the right or on the left. Find a 3 × 3 matrix B, not the identity matrix or the zero matrix, such that AB = BA.