Matrix addition/multiplication with different sizes I have the following two matrices:
$$A=\begin{pmatrix}1 & -2\\3 & 1\end{pmatrix}\text{ and }B=\begin{pmatrix}1 & 3 & 
 2\\-1 & 0 & 2\end{pmatrix}$$
So I have two matrixes with different sizes. Multiple sources tell me that I can't do multiplication or addition with matrix of different sizes. So I'm a bit confused. Can I do it with these? How?


So I have two matrixes with different sizes. Multiple sources tell me that I can't do multiplication or addition with matrix of different sizes.

You can't add matrixes of different sizes as stated by @meshal. Hence, A+B or B+A can't be performed. However, you can multiply them. Here's how:
$$A=\begin{pmatrix}1 & -2\\3 & 1\end{pmatrix}\text{ and }B=\begin{pmatrix}1 & 3 & 
 2\\-1 & 0 & 2\end{pmatrix}$$
$$AB=\begin{pmatrix}1 & -2\\3 & 1\end{pmatrix}\text{ * }\begin{pmatrix}1 & 3 & 
 2\\-1 & 0 & 2\end{pmatrix}$$
$$AB=\begin{pmatrix}1\cdot \:1+\left(-2\right)\left(-1\right)&1\cdot \:3+\left(-2\right)\cdot \:0&1\cdot \:2+\left(-2\right)\cdot \:2\\ 3\cdot \:1+1\cdot \left(-1\right)&3\cdot \:3+1\cdot \:0&3\cdot \:2+1\cdot \:2\end{pmatrix}$$
$$Finally, AB=\begin{pmatrix}3&3&-2\\ 2&9&8\end{pmatrix}$$
