Matrix Operations

7. Example (we will do this example in detail on the next slides:)

   $AB = \begin{bmatrix}1 & 2 \\ 3 & 4 \\ 5 & 6 \\ 7 & 8\end{bmatrix} \begin{bmatrix}1 & 0 & 2 \\ 0 & 1 & 3\end{bmatrix} = \begin{bmatrix} 1 & 2 & 8 \\ 3 & 4 & 18 \\ 5 & 6 & 28 \\ 7 & 8 & 38 \end{bmatrix} = C$

   Fun Class Activity:
   1. Find matrices $A$ and $B$ such that $AB \neq BA$.
   2. Why does this happen?
   3. What type of matrix do we get when multiplying:
      1. Two identity matrices?
      2. Two diagonal matrices?
      3. Two upper triangular (or tow lower triangular) matrices?