<s>[INST] Calculate $A \cdot B$ and say if it's equal to $B \cdot A$ (matrixes) 
Calculate $A \cdot B$ and $B \cdot A$ for $A= \begin{pmatrix} 1 & 1\\ 
1 & 1 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & -1\\  1 & 1
\end{pmatrix}$
Is $A \cdot B=B \cdot A$?

This is a task from an old exam and I'd like to know if I did it correctly?
I will only ask for $A \cdot B$ because the other is done the same way.
        |  1     -1
  A*B   |  1      1
---------------------
1    1  | c_11   c_12 
1    1  | c_21   c_22

$c_{11}= 1 \cdot 1+1 \cdot 1=2$
$c_{12}= 1 \cdot (-1)+1 \cdot 1=0$
$c_{22}= 1 \cdot 1+1 \cdot 1=2$
$c_{22}= 1 \cdot (-1) +1 \cdot 1=0$
Thus, $A \cdot B = \begin{pmatrix} 2 & 0\\ 
2 & 0 \end{pmatrix}$
Is it correct? I would do $B \cdot A$ this way too and then check if they are equal to complete the task.
 [/INST] Your calculation is correct.
Notice that if you were not required to calculate $B \cdot A$ then you would not have needed to calculate it entirely in order to get that $A \cdot B \neq B \cdot A$.
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