Let's solve the problem by finding the sum of matrices $A$ and $B$.

Given: $A = \begin{pmatrix} 3 & 4 \\ -2 & 8 \end{pmatrix}$ $B = \begin{pmatrix} 2 & 0 \\ 5 & 7 \end{pmatrix}$

To find $A + B$, we add the corresponding elements of matrices $A$ and $B$:

$A + B = \begin{pmatrix} 3 & 4 \\ -2 & 8 \end{pmatrix} + \begin{pmatrix} 2 & 0 \\ 5 & 7 \end{pmatrix} = \begin{pmatrix} 3+2 & 4+0 \\ -2+5 & 8+7 \end{pmatrix} = \begin{pmatrix} 5 & 4 \\ 3 & 15 \end{pmatrix}$

Thus, the correct answer is: $\boxed{\text{a.} \ \begin{pmatrix} 5 & 4 \\ 3 & 15 \end{pmatrix}}$

Do you want details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the result of subtracting matrix $B$ from matrix $A$?
2. How do you multiply two matrices?
3. What is the determinant of matrix $A$?
4. What is the inverse of matrix $A$ if it exists?
5. How do you perform scalar multiplication on a matrix?

Tip: When adding or subtracting matrices, ensure they have the same dimensions, meaning the same number of rows and columns.