The inverse of matrix A is $A ^ { - 1 } = \left[ \begin{array} { l l } 1 & 0 \\ 2 & 1 \end{array} \right]$. Given that
$$A \cdot \left[ \begin{array} { l } 1 \\ a \end{array} \right] = \left[ \begin{array} { l } b \\ 4 \end{array} \right]$$
what is the sum $\mathrm { a } + \mathrm { b }$?\\
A) 5\\
B) 7\\
C) 8\\
D) 9\\
E) 11