The question is asking you to calculate $A + B$, where:

$A = \begin{bmatrix} 7 & 3 \\ 7 & 7 \end{bmatrix}, \quad B = \begin{bmatrix} -8 & 5 \\ 5 & -9 \end{bmatrix}.$

Matrix addition is performed element by element. Let's calculate each element of $A + B$:

1. Top-left element: $7 + (-8) = -1$
2. Top-right element: $3 + 5 = 8$
3. Bottom-left element: $7 + 5 = 12$
4. Bottom-right element: $7 + (-9) = -2$

Thus, the result is:

$A + B = \begin{bmatrix} -1 & 8 \\ 12 & -2 \end{bmatrix}.$

Let me know if you need further clarification or assistance!

Here are five related questions to deepen your understanding:

1. How do you subtract two matrices instead of adding them?
2. What are the rules for multiplying two matrices together?
3. What is the identity matrix, and how does it affect addition or multiplication?
4. Can matrix addition be performed if matrices have different dimensions? Why or why not?
5. How does matrix addition relate to vector addition?

Tip: Always ensure matrices have the same dimensions before performing element-wise operations like addition or subtraction!