updates

content/Math4302/Math4302_L2.md

@@ -146,6 +146,8 @@ right cancellation are the same
 > [!NOTE]
 >
 > This also implies that every row/column of the table representation of the binary operation is distinct.
+>
+> _If not, suppose $a,b$ have the same row/column, then we can prove $a=b$ using cancellation from right and left._
 
 3. We can solve equations $a*x=b \text{ and } x*a=b
 $ uniquely.
@@ -156,7 +158,7 @@ $x=a^{-1}* b$, similarly $x=b* a^{-1}$.
 
 Group with 1 element $\{e\}$.
 
-Group with 2 elements $\{e,a\}$.
+Group with 2 elements $\{e,a\}$. (example is $(\{-1,1\},\times)$)
 
 And