Answer
Two matrices may be added together only if they have the same dimensions.
To add two matrices, just add the corresponding elements together.
The sum will have the same dimension as the ones that were added.
Work Step by Step
First, keep in mind that only matrices with the same dimensions can be added together.
For example:
$A=\begin{bmatrix} 1 &2\\3&4\end{bmatrix} $ and $B=\begin{bmatrix} 5 &6\\7&8\end{bmatrix} $
may be added together because both of the are $x\times2$ matrices.
The matrices
$A=\begin{bmatrix} 1 &2\\3&4\end{bmatrix} $ and $C=\begin{bmatrix} 5 &6 &7\\8&9 &10\end{bmatrix} $
cannot be added because $A$ is a $2\times2$ matrix while $C$ is a $2\times3$ matrix.
To add matrices $A$ and $B$, add the corresponding elements to obtain:
$A+B=\begin{bmatrix} 1 &2\\3&4\end{bmatrix} +\begin{bmatrix} 5 &6\\7&8\end{bmatrix}=\begin{bmatrix} 1+5&2+6\\3+7&4+8\end{bmatrix} =\begin{bmatrix} 6 &8\\10&12\end{bmatrix} $
Therefore, the sum of $A$ and $B$ is: $\begin{bmatrix} 6 &8\\10&12\end{bmatrix}$.
