Answer
Calculate $0+A$ and $A+0$.
Work Step by Step
Consider the matrices:
$$A=\begin{bmatrix}a_{11}&a_{12}&...&a_{1n}\\a_{21}&a_{22}&...&a_{2n}\\...&...&...&...\\a_{m1}&a_{m2}&...&a_{mn}\end{bmatrix}$$
$$0_{m\times n}=\begin{bmatrix}0&0&...&0\\0&0&...&0\\...&...&...&...\\0&0&...&0\end{bmatrix}$$
First calculate $0_{m\times n}+A$:
$$\begin{align*}
0_{m\times n}+A&=\begin{bmatrix}0&0&...&0\\0&0&...&0\\...&...&...&...\\0&0&...&0\end{bmatrix}+\begin{bmatrix}a_{11}&a_{12}&...&a_{1n}\\a_{21}&a_{22}&...&a_{2n}\\...&...&...&...\\a_{m1}&a_{m2}&...&a_{mn}\end{bmatrix}\\
&=\begin{bmatrix}0+a_{11}&0+a_{12}&...&0+a_{1n}\\0+a_{21}&0+a_{22}&...&0+a_{2n}\\...&...&...&...\\0+a_{m1}&0+a_{m2}&...&0+a_{mn}\end{bmatrix}\\
&=\begin{bmatrix}a_{11}&a_{12}&...&a_{1n}\\a_{21}&a_{22}&...&a_{2n}\\...&...&...&...\\a_{m1}&a_{m2}&...&a_{mn}\end{bmatrix}\\
&=A.
\end{align*}$$
We got that
$$0_{m\times n}+A=A.\tag1$$
Then calculate $A+0_{m\times n}$:
$$\begin{align*}
A+0_{m\times n}&=\begin{bmatrix}a_{11}&a_{12}&...&a_{1n}\\a_{21}&a_{22}&...&a_{2n}\\...&...&...&...\\a_{m1}&a_{m2}&...&a_{mn}\end{bmatrix}+\begin{bmatrix}0&0&...&0\\0&0&...&0\\...&...&...&...\\0&0&...&0\end{bmatrix}\\
&=\begin{bmatrix}a_{11}+0&a_{12}+0&...&a_{1n}+0\\a_{21}+0&a_{22}+0&...&a_{2n}+0\\...&...&...&...\\a_{m1}+0&a_{m2}+0&...&a_{mn}+0\end{bmatrix}\\
&=\begin{bmatrix}a_{11}&a_{12}&...&a_{1n}\\a_{21}&a_{22}&...&a_{2n}\\...&...&...&...\\a_{m1}&a_{m2}&...&a_{mn}\end{bmatrix}\\
&=A.
\end{align*}$$
We got that
$$A+0_{m\times n}=A.\tag2$$
From $(1)$ and $(2)$ we get:
$$0_{m\times n}+A=A+0_{m\times n}=A.$$
