9×9=81  9×8=72  9×7=63  9×6=54  9×5=45  9×4=36  9×3=27  9×2=18 
8×8=64  8×7=56  8×6=48  8×5=40  8×4=32  8×3=24  8×2=16  
7×7=49  7×6=42  7×5=35  7×4=28  7×3=21  7×2=14  
6×6=36  6×5=30  6×4=24  6×3=18  6×2=12  
5×5=25  5×4=20  5×3=15  5×2=10  
4×4=16  4×3=12  4×2=8  
3×3=9  3×2=6  
2×2=4 
This table does not give the ones and zeros. That is because:
Adding a number to itself is the same as multiplying it by two. For example, 7+7=14, which is the same as 7×2.
Multiplication tables can define 'multiplication' operations for groups, fields, rings, and other algebraic systems.
The following table is an example of a multiplication table for the unit octonions (see octonion, from which this example is taken).
·  1  e_{1}  e_{2}  e_{3}  e_{4}  e_{5}  e_{6}  e_{7} 
1  1  e_{1}  e_{2}  e_{3}  e_{4}  e_{5}  e_{6}  e_{7} 
e_{1}  e_{1}  1  e_{4}  e_{7}  e_{2}  e_{6}  e_{5}  e_{3} 
e_{2}  e_{2}  e_{4}  1  e_{5}  e_{1}  e_{3}  e_{7}  e_{6} 
e_{3}  e_{3}  e_{7}  e_{5}  1  e_{6}  e_{2}  e_{4}  e_{1} 
e_{4}  e_{4}  e_{2}  e_{1}  e_{6}  1  e_{7}  e_{3}  e_{5} 
e_{5}  e_{5}  e_{6}  e_{3}  e_{2}  e_{7}  1  e_{1}  e_{4} 
e_{6}  e_{6}  e_{5}  e_{7}  e_{4}  e_{3}  e_{1}  1  e_{2} 
e_{7}  e_{7}  e_{3}  e_{6}  e_{1}  e_{5}  e_{4}  e_{2}  1 
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