The problem provided is asking to solve for $a$ based on a system of matrix equality. Here's the equation from the image:

$\begin{pmatrix} a + b & 2 - a \\ 9 & 5 - c \end{pmatrix} = \begin{pmatrix} b + a & 2a + 8 \\ 9 & -c + 5 \end{pmatrix}$

We can solve for $a$ by equating the corresponding elements of the matrices.

Step-by-step solution:

1. First Element: From the top-left of the matrix: $a + b = b + a$ This equation is trivially true, so it doesn't give any new information.

2. Second Element: From the top-right of the matrix: $2 - a = 2a + 8$ Solve for $a$: $2 - a = 2a + 8$ Move all terms involving $a$ to one side: $2 - 8 = 2a + a$ Simplify: $-6 = 3a$ $a = -2$

Thus, $a = -2$.

The correct answer is B. -2.

Would you like more details or explanations? Here are 5 related questions:

1. How do we solve matrix equations with variables?
2. What happens if the matrices don't have the same dimensions?
3. Can we apply the same approach to solve for $b$ or $c$?
4. What would happen if the equation for $a$ were quadratic?
5. Can matrix equality apply to matrices of larger sizes?

Tip: When solving for variables in matrix equations, always compare corresponding elements to set up equations systematically!