Let A be a $2 \times 2$ matrix and $I$ be the $2 \times 2$ identity matrix such that
$$A ^ { 2 } = \left[ \begin{array} { l l } 2 & 1 \\ 1 & 5 \end{array} \right]$$
What is the value of the determinant $| ( \mathbf { A } - \mathbf { I } ) ( \mathbf { A } + \mathbf { I } ) |$?
A) 2
B) 3
C) 4
D) 5
E) 6

$$A = \left[ \begin{array} { r r } 1 & 0 \\ - 1 & 3 \end{array} \right], \quad B = \left[ \begin{array} { r r } - 1 & 1 \\ 0 & m \end{array} \right]$$
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