You can make tables that display the products modulo m of pairs of
integers from the set
0, 1, 2,…, m - 1
.
To get a multiplication table modulo m with m = 6
Evaluate
mod6 =
You can also find this matrix as the product of a column matrix with a row matrix.
Evaluate
=
mod6 =
Make a copy of this last matrix. From the Edit menu choose Add Row(s)..., add a new row at the top, choose Add Column(s)..., add a new column at the left, and fill in the blanks to get the following multiplication table modulo 6:
× |
A more efficient way to generate the same multiplication table is to define
g(i, j) = (i - 1)(j - 1)mod6, then to add a row and a column to the
original matrix. A clever way to make this table is to define
g(i, j) =
i - 2
j - 2
, choose Fill Matrix from the Matrices submenu, choose Defined by Function from the dialog box,
specify g for the function, and set the matrix size to 7 rows and 7
columns. You can generate an addition table by defining
g(i, j) = i + j - 2
mod6.