I have been trying to find the answer to this question or for something similar but I cannot find anything on this. Also, I tried looking in the textbook of mymathlab and can't find the problem like it in there either.
I just think I am not setting the problem up correctly.
Here is the statement: Find the product of the sum of A and B and the difference between C and D
I think it's $(A)(B)-(B)(A).$ But obviously, that is incorrect.
Here are the matrices:
$$A=\left[\begin{matrix}1&-1\\1&1\end{matrix}\right],\quad B=\left[\begin{matrix}1&-1\\1&-1\end{matrix}\right],\quad C=\left[\begin{matrix}1&0\\-1&1\end{matrix}\right],\quad D=\left[\begin{matrix}0&-1\\0&1\end{matrix}\right]. $$
You need to find $(A+B)(C-D)$
Sum of $A$ and $B$ $$A+B=\begin{pmatrix} 1 & -1 \\ 1 & 1 \end{pmatrix}+\begin{pmatrix} 1 & -1 \\ 1 & -1 \end{pmatrix}=\begin{pmatrix} 2 & -2 \\ 2 & 0 \end{pmatrix}$$
Now difference of $C$ and $D$ $$C-D\begin{pmatrix} 1 & 0 \\ -1 & 1 \end{pmatrix}-\begin{pmatrix} 0 & -1 \\ 0 & 1 \end{pmatrix}=\begin{pmatrix} 1 & 1 \\ -1 & 0 \end{pmatrix}$$ Now you need to find $$(A+B)(C-D)=\begin{pmatrix} 2 & -2 \\ 2 & 0 \end{pmatrix}\cdot\begin{pmatrix} 1 & 1 \\ -1 & 0 \end{pmatrix}$$ $$(A+B)(C-D)=\begin{pmatrix} 4 & 2 \\ 2 & 2 \end{pmatrix}$$