When you add two $2 \times 2$ matrices, the result will also be a $2 \times 2$ matrix. This is because matrix addition is performed element-wise, and the dimensions of the matrices must be the same for addition to be defined.

For example, if you have: $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}, \quad B = \begin{pmatrix} e & f \\ g & h \end{pmatrix}$ Then the sum of $A$ and $B$ will be: $A + B = \begin{pmatrix} a+e & b+f \\ c+g & d+h \end{pmatrix}$ The resulting matrix is also $2 \times 2$.

Would you like a more detailed explanation on matrix addition or any specific questions about matrix operations?

Here are some related questions you may find interesting:

1. What is matrix scalar multiplication?
2. How do you multiply two matrices of different dimensions?
3. What is the identity matrix for a $2 \times 2$ matrix?
4. How do you find the determinant of a $2 \times 2$ matrix?
5. What are the properties of matrix addition?

Tip: Matrix operations require that dimensions align. For addition, both matrices must have the same dimensions.