If `A ,\ B` and `C` are three matrices of the same order, then prove that `A=B=>A+C=B+C` .

Explanation

$$\operatorname{Let} A=\left[\begin{array}{ll}1 & 0 \\ 0 & 0\end{array}\right], B=\left[\begin{array}{ll}0 & 0 \\ 1 & 3\end{array}\right]$$
And$$C=\left[\begin{array}{ll}0 & 0 \\ 3 & 1\end{array}\right]$$
$$
\therefore A B=\left[\begin{array}{ll}
1 & 0 \\
0 & 0
\end{array}\right]\left[\begin{array}{ll}
0 & 0 \\
...