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

$$A = \left[ \begin{array} { r r } 1 & 0 \\ - 1 & 3 \end{array} \right], \quad B = \left[ \begin{array} { r r } - 1 & 1 \\ 0 & m \end{array} \right]$$
The matrices satisfy the equality
$$\operatorname { det } ( A + B ) = \operatorname { det } ( A ) + \operatorname { det } ( B )$$
Accordingly, what is m?
A) - 3
B) - 1
C) 0
D) 2
E) 4

$$3 x - y = 2$$ $$5 x + 2 y = 3$$
The matrix representation of the linear equation system is
$$A \cdot \left[ \begin{array} { l } x \\ y \end{array} \right] = \left[ \begin{array} { l } 2 \\ 3 \end{array} \right]$$
Given that
$$A \cdot \left[ \begin{array} { l } 1 \\ 2 \end{array} \right] = \left[ \begin{array} { l } a \\ b \end{array} \right]$$
what is the sum $\mathbf { a + b }$?
A) 4
B) 6
C) 8
D) 10
E) 12