2 Unary operations

1. Show for two (preferably non-trivial) matrices conformable for multiplication that
   
   $${\bf (AB)}^{\prime} = {\bf B}^{\prime} {\bf A}^{\prime}$$
   
   

2. If $\bf C$ is
   
   $$\left( \begin{array}{rr} 2 & 6 \ .5 & 4 \end{array} \right),$$
   
   
   find the determinant of $\bf C$.
3. What is the inverse of matrix $\bf C$?
4. If $\bf D$ is
   
   $$\left( \begin{array}{rr} .2 & .3 \ .4 & .6 \end{array} \right),$$
   
   
   find the determinant of $\bf D$.
5. What is the inverse of $\bf D$?
6. If tr($\bf A$) means the trace of $\bf A$, what is tr($\bf C$) + tr($\bf D$)?