Answer
The statement is false.
Work Step by Step
Consider the matrices having $A$ and $B$ of different order:
$A=\left[ \begin{matrix}
1 & 0 \\
2 & 3 \\
\end{matrix} \right]=\left[ \begin{matrix}
{{a}_{11}} & {{a}_{12}} \\
{{a}_{21}} & {{a}_{22}} \\
\end{matrix} \right]$
And
$B=\left[ \begin{matrix}
1 & 0 & 0 \\
2 & 3 & 1 \\
0 & 0 & 1 \\
\end{matrix} \right]=\left[ \begin{matrix}
{{b}_{11}} & {{b}_{12}} & {{b}_{13}} \\
{{b}_{21}} & {{b}_{22}} & {{b}_{23}} \\
{{b}_{31}} & {{b}_{32}} & {{b}_{33}} \\
\end{matrix} \right]$
Then, ${{a}_{11}}$ is added with ${{b}_{11}}$, ${{a}_{12}}$ is added with ${{b}_{12}}$, but there is no corresponding element in A that can be added with ${{b}_{13}}$.
Therefore, two matrices of different order cannot be added.
